Itinerary help for approx 3 weeks in September 2022 in Greece

Spend two nights on overtouristed Santorini to see it’s views and then visit Paros or Naxos to have a more Greek experience.
Consider Crete which is the largest. Stay in Chania and explore western Crete by car. Spend a few nights on the southern coast in Loutro., leaving car in a lot in Chora Skafion and taking ferry to Loutro.
Include Corinth on your way to stay in beautiful Napflion which is surrounded by some of Greece’s most famous antiquities. Spend four nights here. There is lot more on the Peloponnesean peninsula to visit- Mystras,Monemvasia, and ancient Olympia of course, more goosebumps!
Beaches? Peloponnesean has some, Oaros too. Crete has Falasarna and Elafonisi among many others. Santorini is not known for it’s beaches.
Napflion and Chania are Greece’s two most beautiful small cities.
We ate fresh fish almost every night. Grilled, lemon and olive as a sauce. The chicken in Greece is exceptional too. Add a real Greek salad( huge so share one) and you have a great meal. Eating in Greek tavernas is part of the culture and I would encourage you to eat dinners in them most of the time. Desserts are usually offered free, like honey nut cake.
We have been to Greece twice, once for a month, and can’t wait to return!

Sleep in Athens for four nights if you’re taking a day trip and then fly nonstop to Santorini for three nights. From Santorini take a direct ferry to Heraklion: https://www.anek.gr/en/routes/ but it’s too early to tell what the schedule will be in Sep. Right now, there’s one operating once a week departing Santorini at 4:10a taking 6h and I don’t see any nonstop flights between Santorini and Crete. From Crete you can fly from Chania (CHQ) to Rome nonstop but not everyday on Ryanair.

Experienced travellers to Greece generally suggest you get out to your first island on arrival. Even at 19:50 there is a good chance you could make the last flight of the day which is 23:10 in Late September. to Santorini. You need 2 hours to make the connection.

However since you are planning to fly from Crete to Rome and not return to Athens for the end of your trip there is no reason for you not to do Athens first.
Athens https://www.flickr.com/photos/stanbr54/albums/72157632121475515
While you are touring in Corinth make sure you see Ancient Corinth and the nearby fortress of Acrocorinth and perhaps Ancient Nemia.

Corinth Area. https://www.flickr.com/photos/stanbr54/albums/72157711755443483

Perhaps after your Athens visit 3 days is recommended you might consider going to Corinth and then heading south another hour to Nafplio. Its a lovely seaside city. Just make sure you find a hotel in the old city.
Nafplio is a city that Athenians visit for weekend get aways.
Nafplio https://www.flickr.com/photos/stanbr54/albums/72157632094108982

When you are ready to island hop I would suggest your ferry or fly to Naxos. Its a lovely island that will give you a wonderful Greek experience. By late September you might want to stay at St George beach. It is part of Naxos town so you get a beach vacation with all the activities of the town.
Naxos town https://www.flickr.com/photos/stanbr54/albums/72157632094558042
Trip around Naxos https://www.flickr.com/photos/stanbr54/albums/72157634605629689
Naxos sunsets https://www.flickr.com/photos/stanbr54/albums/72157700728046481

Naxos is a short ferry hop to Santorini about 2 hours. We have stayed for 3 nights, thats about all the time my budget can stand.
This is the island you will want to splurge and get a hotel with Caldera view.
Santorini https://www.flickr.com/photos/stanbr54/albums/72157632154800782

After Santorini take the afternoon ferry to Heraklion Crete. It will get you in around 7pm so plan to spend the night in Heraklion. The central area has a great evening promenade when everyone walks around visiting bars and tavernas. If ancient sites are important to you you could visit Knossos and perhaps a day trip south to Phastos and Gortyz. Gortyz is amazing. There is a whole Roman city half buried in olive groves.
Heraklion https://www.flickr.com/photos/stanbr54/albums/72157655935354556
Gortyz https://www.flickr.com/photos/stanbr54/albums/72157666456665788

Then transfer to Chania area in west Crete.

Chania https://www.flickr.com/photos/stanbr54/albums/72157632117917828

I am happy to prvide more details if there is something in my suggestions you would like additional information on.

Thank you so much for all the suggestions! Very helpful! I may have more questions later.

stranbr is right, the best you could do is in this order:
3 or 4 days in Athens (+ excursions), then
Take a plane or a ferry to go to an island.

Since stanbr is a Naxos lover (he's not wrong) he recommends Naxos but you can also go to another island on the route between Athens and Santorini.
Paros, Sifnos, Milos and Amorgos are also possible choices.
Paros and Milos also have an airport.

From this island you can take a ferry to Santorini (in the Cyclades there are no direct flights between islands) and spend a maximum of 3 days there.

And finally take a last ferry to Crete.

Regarding the allocation of days, do not be afraid to spend time in Crete, it's a very large island where there is a lot to do and see.

Hello from Wisconsin,
Over touristed Santorini... If you want to minimize tourists and have a beautiful island, try Sifnos. Too small to handle cruise ships, big enough to have restaurants and some other amenities.

wayne iNWI

Thank you for all the great tips and suggestions. We've revised our itinerary to this:
Athens - 2 days plus a day trip to Corinth
fly to Naxos for 3 nights
ferry to Paros for 3 nights
ferry to Santorini for 3 nights
ferry to Crete for 7 nights, dividing our stay between Heraklion and Hania

When would you suggest that we buy ferry tickets to Paros, Santorini, and Crete? Before we leave on our holiday or when we get to the islands?

There are enough ferries possibilities for the island hopping you want to do. You won't need to book far in advance.

Since you start by taking a flight to Naxos, you can buy the ticket to Paros when you are in Naxos and do the same for the following ferries unless you don't want to have to go back to a ferry ticket office every time you are on an island, in this case you can buy all the tickets for the following journeys in the first ticket office.

Note that if for any reason you do not want or cannot go to a ticket office, most of the time you will also have the possibility of booking online (Web-Checkin) and receive your tickets on your smartphone or tablet.

And since you will be traveling a lot by ferry, don't forget to check the weather forecast for the next few days.

I'm sitting on our balcony right now in Kastraki looking at a view of the Meteora area which is about 3.5 hours north of Athens. I can't describe it in much detail. 5 monasteries on 5 spires. Tomorrow we're going on a hike with a guide recommended by one of Rick's guides, Niki. We're also taking a monastery tour from a guide recommended by Niki as well. It's becoming a bit overcrowded, just like everywhere, although in September it may be less crowded. As for Athens, I recommend the Acropolis and the Metropolis, taking tours from Athen's Walking Tours. We took one of the Acropolis & the Agorra, then a food tour from Irini of Athen's Walking Tour as well. We stayed at The Zillers which is close to the Plakka (way overcrowded....thank you cruise tours) and Psyri districts which the latter is eclectic. We could used 1 more day to visit the Acropolis museum. So at least 3 full days. The Ziller's Hotel has great views of the Acropolis and the Metropolis church. In a day or so we head for Delphi for a partial day to tour the ruins there. Then off to Olympia and down the Peloponese. We're going to try to fit in Hydra as Rick says it's one of the best sites for ruins. We'll save the islands for another time.