In the following text I will try to give you an overview and ideas how to plan a holiday up to several weeks in Greece. Based on my own 3 weeks holiday I will give suggestions where to shorten, where you can extend so in the end it is hopefully quite flexible and everyone can just decide which parts are worth it and what might be of less interest.
First question what you want to see and how long there is time. Greece is quite big: there is the mainland with Athens and mountains, Peloponnese peninsula connected via the Isthmus of Corinth with central Greek part and then there are many, many islands where several are worth staying for a week or more themselves (Crete and probably any other if main aim is sea and relaxing). But we wanted a nice picture of culture, mountains, sea, main tourist sights and some calmer areas. Best idea is to start either on islands or the mainland and then end up with the other to save on one flight or ferry and especially save on time. We ended on the Cyclades islands to have the relaxing part in the end and as there were flights home from Santorin. The whole trip took part in September 2020, so during the Covid-pandemic but it worked very well.
All info might change, so happy if you provide more tips/tell me wrong information; if something is unclear feel free to contact me!
source: mapy.cz; here the editable version.
It is a bit difficult to combine our trip with the additional options so I will just start with ours, add some info during the schedule and then add more in the end.
Till Day 1: flying into Athens (on card point number 15), Athens sightseeing, we had three nights there. If you´re efficient and do not need every museum then two full days were enough. Things to do there:
Athens tips
Acropolis /Parthenon: 
when you here about Athens, what come first in your mind, will be probably the Acropolis. Actually acropolis is only the name of the whole hill/citadel and the famous temple is called Parthenon, even more than one acropolis theoretically exist as it only means "highest point of a city", but I think everyone refers to the Athenian one. The regular entrance fee is 20€, but there is also a combined ticket for 30€ for all the other archaeological sites (agora, Olympeion, Hadrian´s library) combined. As long as you have enough time, this would pay off in my opinion. During winter there is in general cheaper entrance fee, so another reason to travel off season!
Acropolis museum: 
located just next to the Acropolis, the museum houses many statues and models to show you the history and development of the Acropolis. Especially when you are an EU-student I can recommend going there because the entrance is for free. Normal price depending on season between 5-10 so also affordable.
Panathenaic Stadium: 
it was already used as a stadium during ancient times but then it declined but was then beautifully reconstructed for the first modern Olympic games in 1896 in Athens. For the games in 2004 it had a smaller roll but was still used as a stadium to let the marathon and other long distances competitions end at such an iconic place. One of the biggest single events held there was a basketball final in 1968 between AEK Athens and Slavia Prague, where around 80 000 people watched the game. Entrance fee for adults 5€ and it includes a great audio guide in many languages and for everyone being a little bit interested in Olympic games I can highly recommend going there!
Kap Sounion: 
we did the Kap Sounion with the car at the end of the road trip but it is also possible to going there with publics from Athens for half a day. Another possibility is sleeping at a hotel just next to it, there is also a beach so you can combine an amazing temple and swimming super close to Athens. Organized tours are probably also available, just search for them in case.
Exarcheia: close to Syntagma square but to the other direction of the main touristic stuff lies the neighbourhood of Exarcheia. It is known for it´s anarchist history and hosted several important events of the recent Greek history: between 1967 and 1974 the NATO-country Greece was ruled as a military dictatorship with the blessing of the US. One of the biggest uprisings against this regime took place in Exarcheia with students of the Polytechneion university and many more people protesting. The regime beat down the students using tanks, more than 2000 people were arrested, around 24 people died. Just one week later as a result from the protests a even bigger hardliner staged a counter-coup but finally the dictatorship ended in 1974.
The second time it hosted clashes between protestors and police was in 2008: a 15 year old was killed by a special officer and sparked off protests and riots. Rising frustration of the young generation during the global economical crisis supported the developments. These protests are repeated every year and it is also said to be a sign to show the police that they still depend on its citizens, still every year cars are burning and people get arrested. But outside these protests it is a very vibrant and young neighbourhood, many students and migrants since the refugee crisis, with bars and a good nightlife!
Psyri: 
after being dodge for a long time it got gentrified over the last years and hosts now many, many restaurants and bars. When we were there we mainly heard Greek, so to dive deeper into Greek lifestyle rather search some restaurant around here than something straight around the Acropolis. Plateia Iroon is the main square and from there into all directions the gastronomy is spreading. We went for lunch to the tiny restaurant Avli it´s a bit offside the main road and nicely hidden in a yard of a house without any advertising or waiters annoying you with their menu. First day we heard many loud voices and guitar playing so thought it is a private party but when we figured out it is a restaurant we decided to go there the next day. The menu is rather small (and cheap), had a mixed plate and was really good. Best was the atmosphere, nice sheltered from all the houses and just the narrow yard and all around us only young Greeks and we were definitely the only tourists there at that moment. I think the whole neighbourhood is also nice for accommodation: close the historical stuff but more lively around.
Day 1: picking up the car at the airport (alternatively city centre but decided it is more convenient avoiding city traffic and also for returning as it is close to Kap Sounion our last stop). Then via the highway to Isthmus of Corinth (2), just off the highway for a short stop there (there are signs are a big parking lot so not difficult to find). 
We continued the same day all the way to the peninsula of Lefkada, therefore skipping whole Peleponnes, partly because other areas seemed more tempting but also because I have been already there some years ago (Nafplio, Olympia). Patras we also skipped and just used the famous Rio–Antirrio Bridge to cross back to mainland Greece. It is one of the longest multi-span cable-stayed bridges and due to the danger of earthquakes a true architectonical masterpiece. On the way there was quite a lot of highway toll to pay, more than 20€ throughout the day but this highway is just way faster than staying on mainland and Corinth plus the bridge around Patras are probably already reason enough going there. In the evening we arrived on Lefkada (3).
Lefkada tips
Very close to Zakynthos but via a swimming bridge/road connected to the mainland and therefore easier to reach lies the island of Lefkada. 
We stopped there for 24h and did quite a lot there, but retrospectively seen I think I´d either stay longer or skip it completely to safe some time. It´s super popular for Greek tourists, so I´d say better than some of the neighbouring islands without drunk English speakers. Lefkada itself is very hilly and has some mountains rising more than 1000m from sea level in the middle of the island so I suppose it also interesting for hiking but did not do anything like this there although it seemed quite tempting.
Porto Katsiki: 
is the most famous beach on the island and quite similar to the famous smuggler´s beach with the ship wreck on Zakynthos. In the morning around 9am we were the first but till lunch it filled up, luckily no boats arriving with another bunch of people (off season and corona have advantages). What we did not keep in mind is the amazing cliff covering the beach and making it famous: it also puts a huge shade over it and just around lunch time the sun appears. So better starting there later (or if it´s incredibly hot using the mornings then). Water was amazing, super clear, many rocks to climb on. Agremni beach is the name of the other famous but we had only time for one so cannot say much more.
Nydri waterfalls: 
located at the inside of the island it is a waterfall when there is no drought beforehand. The walk there is very pleasant through nice rock formations but during our visit it was just a joke of a waterfall due to the lack of water.
Vasiliki: we slept in that town. It has a beach and is very close to all the sights we wanted to do so thought it´s quite time efficient staying there. There are several bars, restaurants and a small supermarket so was just sufficient for the night. There is also a new road to the Kap.
Kap Lefkada: 
at the most southern point of the island lies the Kap Lefkada with a light house. Just the ride there is already worth it seeing the great cliffs to your sides and from the Kap there are views towards Ithaka (the island where Odysseus might have came from) and Kefalonia. Sunset might be amazing from there but for this you need a clear sky (which we obviously did not have), bring some snack and enjoy it. Also with covered sky I would not miss out that point, especially as it is close the Katsiki and both things can be easily combined.
Day 2: After going to their most famous beach (see the tips), we jumped around noon into the car and continued all the way north up. We decided to do some stopovers but still to drive to the Vikos canyon in the evening/during night to have it more relaxed the next morning. But sleeping over somewhere on the way is definitely also a good option! So on the way up there is the source if the Acheron river (4), this was in the Greek mythology one of the three rivers surrounding the underworld. Somewhere I read that Achilles was put there into the water from his mother but this should be another river. There you have quite some nature activities, hiking through a gorge, kayaking etc. We just had a very short stopover, walked to the source and then back to the parking lot. Took in total like an hour. Afterwards driving to Parga (5): 
it is often described as a secret tip off the main touristic paths. I can imagine that this refers to international visitors but for Greeks it is not true and at the cute seaside there are many, many restaurants and souvenir shops. Amazing view to the sea straight from the terraces and cute, narrow streets are making it definitely also worth for staying over night. But we decided differently and were on a stricter schedule so still continued further up north to Vitsa (6) around the Vikos gorge.
Vikos tips
The best in this area is that all villages are incredibly cute! Just stone houses, paved roads, no "normal" houses. A pleasure just wandering around the small streets. Around there is the Vikos-Aoös national park, with the mountain range Tymfi. The highest point is 2497m and called Gamila.
Vitsa: some 20min away from the main town of Monodendri, we sleep two nights in the hotel En Chora Vezitsa. Can only recommend it. Location just great just next to the church and main square, breakfast was with great Greek yoghurt (unfortunately never got anywhere else something as good as that one) and they also have a restaurant which has just awesome food. Only local ingredients from a surrounding of 20km, had great lamp from the grill. Just the location at the main square, shaded from a big tree and a view direction of the canyon is amazing. All bones were eaten by their dog so the plate was more than clean afterwards. Thessos, the owner, was very helpful with our next planning. He himself is a mountain guide so if you need more info or want to book something just contact him (I suppose also without staying at their accommodation). For the taxi ride back from Vikos to the hotel it was cheaper though just asking random locals but just ask beforehand before leaving, then you can compare the prices and still have the security that something will bring you back for sure.
Vikos canyon: the hike through the canyon usually starts in Monodendri from where you will walk down to the ground of it. If you stay in Vitsa it is no problem either, just a little bit longer. The whole path is nicely marked with red signs and in the end not really difficult to miss anything because you just follow the river. 
We got once lost though because we were too close to the river and not on the hiking path anymore, if this happens just turn around to the last sign and try again, there were enough signs. Something to keep in mind is the weather: in spring there is the snow melt and therefore I read there can be a lot of water and some passages even not passable anymore, in September it was completely dry and we could have walked just along the empty river bed the whole time. This means on the other hand that there is not much water and you should bring enough. If I remember correctly at the first part there was a spring where you could refill your bottles but better bring enough. Close the village Vikos there lie the Voidomatis springs in the gorge, when we were there they were dry as well. Was funny to see though that several people went down just to see these, when you already go there try to walk the whole canyon to get a better experience and then you still have the springs at the end on your path. We ended then in Vikos and went back up to civilization. That is a crossroad with signs to Vikos and Papingo so it would also be possible to continue even further but then the ride back gets also longer.
In Vikos we just went to some restaurant and asked which options we are having to get back to Vitsa, apparently some official taxi just left, so some old guy drove us back for 50€, unfortunately he did not speak any English but tried his best being a good guide/driver and told us the names of all towns which we saw on the way.
Drakolímni lakes/refuge D.Georgoulis from Mikro Papingo:
although Thessos told us it is only a half day trip just with keeping the distance and vertical metres in mind it is rather a day trip if you are not a trail runner. Highly recommendable though, the hut serves food and drinks and also answers all your questions where to continue and which options there are. The hike starts just from the end of the road in Mikro Papingo and if you want to make it shorter just go till the hut, from there it was around an hour further to the lake. From there you will find a great view towards the mountain range and all its highest peaks.
Stone bridges: the whole Zagora region is famous for its stone bridges, the one we visited is just an hour walking away from Vitsa.
Viewing point: Oxi is maybe the most famous viewing point into the Vikos canyon. We drove there as well, just following the street up from Monodendri and its indeed amazing views seeing the three arms merging. On the way as usual in the Greek mountains many sheeps and shepard dogs on the way accomponying and blocking the cars.
National park: the whole area is located within the Vikos-Aoös National Park, founded in 1973 it covers parts of the Pindus mountains. The Voidomatis was carving the Vikos gorge (12km long and up to 1000m deep), the Aoös the less famous Aoös gorge (10km) long. The river then flows towards Albania and its name is changing to Vjosa. Right now there are local initiatives, supported by Patagonia who also created a 6min long film, to transfer the Albanian part of the river into a national park. It should avoid the construction of dams and preserve one of the last wild, unregulated rivers in Europe.
Day 3: From our accommodation we hiked to Monodendri and then down to the canyon and all the way to the town Vikos. From Vikos there should be some kind of taxi, locals told us that it just left so a old guy offered to ride us back to Vitsa for 50€ for two. Read online that sometimes it was 10€ cheaper but in the end it does not matter too much, the car would never be allowed to go on the road in other areas but for some remote mountain areas it works still enough. The hike took around 6h, the ride back 30min.
Day 4: As plans for later got postponed for a day we could use the day for another hike and started from Mikro Papingo (7), after the hike we drove to the Meteora monasteries. There I would recommend to sleep in Kastraki (8) and not in the bigger city of Kalambaka as it is closer to the monasteries and most hotels already have views to the monasteries.
Meteora info
The monasteries were founded in the 14th century, originally they were only supplied with rainwater, nowadays they are connected to the normal water/electricity supply.
Every day of the week some monasteries are closed so if you stay there only one day there is not the chance of visiting all. The question is as well though if it is really worth checking every single of them as they are quite similar in the end. To each you pay 3€ entrance fee, legs and shoulders need to be covered but they differ a bit how strict everything is handled. It is said the all-female/nuns´ monasteries are stricter. We visited the first 3 ones from the following list:
Holy Monastery of Great Meteoron: it is the oldest and largest of the monasteries so it was for us an obvious choice to visit this one.
Holy Monastery of Holy Trinity: other tourists recommended us this one as it is one of the smaller, more remote and more difficult to reach ones. There is even a walk from the Kalambaka for around 3km to this one or alternatively just from the parking lot quite some stairs. It has a cute small garden and it was also used for shooting the Bond movie "For your eyes only".
Holy Monastery of Rousanou: it is close to the towns and run by nuns, as we wanted to see both monk´s and nun´s ones we started in the morning straight with this.
Holy Monastery of Varlaam: we did not visit this one, from the outside I think it looks the best of all of them. It is just next to the Great Meteoron so the views to everything around will be quite similar.
Holy Monastery of St. Nicholas Anapafsas: the closest monastery to Kastraki and we could nicely see it from our accommodation.
Holy Monastery of St. Stephen: this is also run by nuns. We did not visit it, other travellers we met said it is not that special and as it is the easiest to reach, just a short walk from the parking lot it is also the most crowded one. Which means on the other hand if you have problems with walking stairs this is definitely the best choice for you!
Accommodation: we stayed in the guesthouse Papastathis. Very nice owner, she spoke very good German and as well English and was happy to provide us with info. We just checked online which are still having capacities and went there straight away without reservation, got it then a bit cheaper than online as well. I would definitely recommend staying in Kastraki. From cheaper guesthouses like ours to more expensive ones (the Hotel Doupiani was recommended by a British couple we met), there is a big variety and a direct view towards the monasteries is just awesome.
Sunset spots: I have the feeling that since Instagram grew that much in popularity also sunset pictures are way more hyped. Not only in the mountains you can get nice impressions but also Meteora is famous for it, around the Holy Trinity monastery are some parking lots where you can enjoy a good view. For examples this.
Day 5: The whole day we attributed to the monasteries. We visited 3 out of the 6, which still exist.
Central Makedonia, sights between Meteora and Thessaloniki
We ignored most of them due to time issues but here you can add easily 2 days for these things and see some more on the way. Either if you´re interested into ancient Greek history (Philip II and Alexander the Great) or into nature there is quite some more stuff to do, all recommendations came from a Greek friend who is from this area.
Vergina (9): there is the archaeological site of Aigaim which was the original capital of the Macedons and king Philip II was killed there. From him his son Alexander the Great took over and extended the empire very far to the East. There is a museum and the tomb of Philip II, which was just discovered in the 1970s and in comparison to many others found untouched.
Pella: became the new capital of Macedonia and is also the birth place of Alexander the Great. Today you also find archaeological sites there.
Pozar baths: thermal baths.
Edessa waterfall: as name says: waterfalls. When you are already around worth a visit but to be honest, I have seen more interesting ones in my life.
Here is the second part (2/4 of the total trip) of the roadtrip (to have shorter loading times the road trip is seperated on two parts)