Itinerary for 6 day trip to Greece

We would prefer less touristy if possible.

The most touristy islands in the Cyclades are, In order of popularity:

Santorini

Mykonos

Paros

Naxos

Milos

(This leaves you with 15 other possibilities)

Other very popular tourist islands not in the Cyclades:

Hydra

Rhodes

Kos

Skiathos

(This leaves you with about a hundred other possibilities)

On the mainland, the most touristy places besides Athens are:

Delphi

Meteora

In the Peloponnese: Nafplio (and Epidaurus/Mycenae)

Olympia

Monemvasia

This leaves you with several hundred other possible places

Therefore, any advice suggesting one of these places will, by definition, not match your request.
Which won't be very convenient if you want to see some of the most beautiful and renowned places in Greece.

Where are you coming from. Will you be jet lagged after a transatlantic flight? Give us some information about your wants and plans and perhaps we can whittle away some of the options Jo provided.
2 days in Athens only gives you 4 days for the rest of your trip. Is there any way you can extend your stay.

Jo-Lui has noted that it's impossible to answer your question, when starting from Ground Zero in your knowledge of Greece, and also without any information about your trip length. For instance, are you arriving after a 16-24 hour journey from N America, with resulting fatigue/jet lag, which will severely hamper fast sightseeing... or is this a segment of a much longer European visit, in which you plan to give Greek a quickie look-see?

You might consider a one-time deep-dive into one of the best websites of Greece information, well-organized, along with a look at a map of Greece -- showing that even reaching one island & returning could eat up several of your limited days.

https://www.greecetravel.com/index.html

http://www.greektravel.com/greekislands/

https://www.greektravel.com/maps/greece.html

Thanks for your replies
We will not be jet lagged as we are travelling in Croatia before Greece We have virtually no idea of what to see in Greece. We try not to be part of the overtourism problem. I was thinking of travelling to an island and staying there or to the Peloponnese area picking one place to stay in and venturing out from there.

I wonder how you're going to avoid mass tourism in Croatia. For the past few years, it's been the new must-see destination in Europe. Split and Dubrovnik, from what I've read, have significant environmental problems due to tourism, with the overexploitation of water and energy and uncontrolled overpopulation. I've seen that they're creating artificial beaches to satisfy the growing demand.

In Greece, there are thousands of places where you won't see crowds of tourists, but I wonder if that's really the kind of place you want to go. I know a couple with two kids who just got back from a month in Greece, in a small village of 600 inhabitants near Kalamata, through a home exchange program. I suppose that in four days that's not what you're looking for. You'd need a car anyway.

In the Peloponnese, if you go to Nafplio, for example, it's very easy to avoid the crowds. Just don't go to the old town, which now has only about 150 permanent residents, all the others have moved elsewhere. I've seen watching a Greek TV channel that the Greek authorities are having trouble finding some of them because they've abandoned their homes, which are falling into disrepair. The few thousand people who wander the streets of the old town are either tourists or people working in the tourism industry. But if you stay in the new town, about a kilometer away, you'll mainly see local Greeks living normal lives without seeming to be victims of mass tourism.

Regarding an island easily accessible from Athens and relatively untouched by tourists, you could go to Tinos. You just need to go to the port of Rafina, located 20 minutes from Athens airport, and take a ferry; you'll be in Tinos in 2.5 hours. Easy!

But once on the island, you'll also need a car.

Tinos:

https://photos.app.goo.gl/DBjAgwbAcuH5Pjuk9

We have virtually no idea of what to see in Greece. We try not to be
part of the overtourism problem. I was thinking of travelling to an
island and staying there or to the Peloponnese area picking one place
to stay in and venturing out from there.

I think you are putting the cart before the horse. First figure out what you want to see in Greece--and what can be seen with only six days. The only effect I can see it having on Greece is that I have little interest in going to Santorini or Mykonos or the large resorts that likely mar some of the shores. I went to the Peloponnese in 2019 and I practically had sites to myself--maybe that has changed a lot in the last few years?
The Bradt Guide was really helpful in my trip planning.
I would not worry too much about the overtourism issue. I go where I want to go and I just do the best I can. I completely understand I am part of the problem but this is the life I got and I am going to go see stuff when/while I can.
In Croatia, they have to make artificial beaches because there are not beaches otherwise. I suppose people whine about the rocks. I agree Croatia is where I would try to get off the beaten path because the scenery is equally distributed everywhere. In Greece, you are presumably going to see things that have been on the beaten path for centuries--go see what you want to see!

I agree with the other posts--if you don't already have a list of things you're interested in seeing, first, you should just Google or ChatGPT "top 20 sites to see in Greece" and see if any of them are of interest to you. Most that hit the top 10 will probably be located in Athens, but if there are others, you might need to choose a second "home base".

My first time in Greece, I did 1/3 of my time at each place: Santorini, Naxos, and Athens. Flew straight into Santorini, because I thought, "At least once!" (and you can bus or walk everywhere) Then, we took the slow ferry between Santorini and Naxos--where we rented a car and saw the historical sites there (many of which you just drive up to), and you can ferry to nearby islands quite easily. Then, took fast ferry back to Athens--and did the whole Athens thing.

For a country that is technically the size of Alabama, it is incredibly dense--filled with history at every turn, and getting anywhere takes longer than you think. I just spent 3 more weeks there this summer, and still feel like I have not really even begun.