Greek island recommendation

If your plan is to fly to an island from another country you are dramatically limiting your choices of islands. Many of the islands only have flights from Athens not from foreign countries.
You know where you are flying from.
Just do a google search for direct flights to a Greek island. Crete, Rhodes and Santorini come to mind as likely destinations on direct flights from another country.
If you plan to fly to Athens then connect to another island then you have many more choices.
I like the comment your are young seniors. I will have to remember that one.

I visited in October, flew into Heraklion and went straight to Chania for 5 lovely nights. I went to the local outdoor market, had afternoon cocktails at a bar or cafe on the Venetian harbor, wandered through narrow winding alleyways and explored charming (yes, really) tourist shops. Twice I ate in a restaurant with live entertainment, went to interesting museums and a lovely park with a tiny zoo. I watched locals drinking coffee and playing endless games of backgammon at the cafes that line the seashore. Then I went to Heraklion for 2 nights, mostly to see the archaeology museum and the ancient ruins of Knossos.

The only difficulty was getting from city to city. I decided to save money and took buses. That was a mistake, even for a solo traveler. I had to take a bus from the airport to the city bus terminal, then buy a ticket and find the bus to Chania, which was on schedule and took about 2 hours with only a couple of stops. I still had to take a taxi to the edge of the historic center, and walked to my hotel. On the return trip, instead of 2 hours, the bus took over 4 hours and another taxi to my hotel.

I also went to Santorini and Naxos. Santorini was a zoo - end of the season and still way too many tourists. Naxos was restful and quiet. Of the 3, Crete is definitely your best option.

You first have to find an island that has an airport then decide which of those islands meet your needs.

Here's a website that will show you what islands have airports. Just put your curser on one of the islands with a "dot"

https://en.aegeanair.com/destinations/route-map/

After you find one that will work for you then you can come back and ask for advice.

If you could specify which country you would like to fly from it would be easier to give you relevant answers.

Some of the islands with airports that you can see on the Aegean Air map have direct flights with some European cities
For the most part these are seasonal flights (generally from May to October). So you could also specify what time of year you want to travel.

When I look at your message history and see that you have rented a car on other trips to Europe I wonder why you don't want to rent a car in Greece. Some islands have a good bus network, on others it can be very limited or even non-existent.

I also see that you love markets. There are local producers but very few markets in the Greek islands. Local products are generally not abundant enough for this.

Given that there are beaches everywhere on the vast majority of islands, asking for an island with "good beaches" is like asking if there are any good buildings in New York City. So I also wonder what you consider to be a "good beach"

As an add-on to Tommy's suggestion . . ..

A few of the island airports are international, some are not and only have routes to Athens.

If you know which airport you will be flying from, go to the wiki page for that aiport. You'll find a table listing all the airlines and destinations using it.

We spent 4 nights on Crete this past June. Loved it but not enough time to really explore. We landed in Heraklion and stayed near Rethymno. We rented a car at the airport and driving around was pretty easy. Apple maps and Carplay work flawlessly. I would highly recommend a rental car to minimize wasted time on buses.

We've been fortunate to spend a total of 6 weeks in Greece, including the islands of Hydra, Naxos, Milos, Santorini, and Mykonos. Of those, the only one we revisited was Naxos. It's an easy flight from Athens and it's on the ferry route. (tip here: sign up for the Agean airlines newsletter. They send out information about sales, etc.) The biggest plus for us is that cruise ships don't go there! (nothing ruins a beautiful island like a hulking cruise ship in the harbor!).

The Blue Flag beaches on Naxos are beautiful and close to town. If you want to go further south, the bus is very easy to navigate and inexpensive. Every beach offers cabanas for rent (maybe 5-10 euros). The main town in Naxos has many restaurant options and there is some really cool sight-seeing.

Matt Barrett's guide to Greece is a useful document. He splits his time between NC and Greece.
https://www.greecetravel.com/

We love Greece and can't wait to go back! Enjoy your trip!!

Yo Helen,
Maybe check out Folegandros?
Ferries depart from either Athens (looooooong) or much closer Santorini.

I am done. the fellow Torontonian also currently suffering excruciatingly muggy weather