Greek Islands

The only island in Greece I have traveled to is Crete. There is the Lonely Planet guide to Crete, and the Rough Guide to Crete. On Crete, Heraklion is under-rated by many but there I saw the remains of Knossos, the archaeology museum, the marvelously renovated Koules Venetian fortress that I paid to go inside, passed by the reconstructed town hall, and so on. Look up the Battle of Crete in World War II. Chania has a the maritime museum, another Venetian fortress but you can't go inside, and a little bay crowded with tourists. I didn't make time for rethymno or the Samaria gorge - those are good places. I didn't make time for Santorini - it looks like a good place. I guess few natives on Santorini would be rushing to a job in an office, while Crete has cities where people rush to jobs and life is like many other places.

With only 4 or 5 nights your best bet is to just do one island. Island hopping takes more time than one might expect and you pretty much loose a half day for every island hop.
After your island visit you likely would want to be back in Athens the night before your flight home.
How do you plan to get to your chosen island. Ferry travel from Athens port takes a fair amount of time so you might want to choose an island with an airport.

We have been to Naxos, Paros and Milos on several different visits. All three have airports so you can fly on the first flight of the day and be in your hotel by mid morning.

Our favourite island is Naxos. It has rugged mountain terrain with lovely villages. There are excellent beaches a smattering of antiquities and an interesting old town topped by a Venetian era Kastro.

Here are some images to see what it is like.
Naxos at night
https://www.flickr.com/photos/stanbr54/albums/72177720318406428/
Naxos town

https://www.flickr.com/photos/stanbr54/albums/72177720318203165/

Trip around Naxos https://www.flickr.com/photos/stanbr54/albums/72157634605629689

We are in our early 60s and uninterested in the party scene

Don't worry, the only Greek island that is a party scene is Mykonos. This is what makes it successful.
Even if you also eliminate the very popular and crowded Santorini you still have at least 15 other visitable islands in the Cyclades, all with white washed houses, blue domes, windmills and beautiful beaches.

And many more than 100 other Greek islands in other parts of the Aegean Sea.

I agree with stanbr, 4 or 5 nights is only 3 or 4 full days.
After a very busy archaeological tour you will need to settle down and not repack / unpack after 48 hours in one place, so go to a single island.
Even the smallest Greek island requires at least 4 days to partially know it.

...would like to experience the uniqueness of the Greek islands, good
food and some cultural touchstones

All the Greek islands are unique, I have visited quite a few (I stopped counting) and no island is like another, as long as you take your time to explore them, by walking, driving or sailing.

You have time to choose:

https://www.visitgreece.gr/islands/

@stanbr and @jolui, what terrific responses. So appreciated! We've decided on Naxos! Thanks so much for your time.

You have made a great choice in Naxos. We were there in Mid June this year . Its a great time to visit particularly the first couple of weeks. There are enough people around to make it interesting but not crowded. The major beaches had lots of people but again not crowed at all.

One tip. If you choose a taverna to dine in the evening be sure to make a reservation. In the past that was not necessary but now its a good idea.