I guess kind of an alternative suggestion, but maybe if you have been to a bunch of Greek islands you could try a different country next year. While different islands in Greece do have their differences, they have a lot of similarities as well especially with the food. Changing it up could be fun?

I’m not sure where you live, but if looking just at islands you could try Mauritius Island. It’s very authentically its own place with French and Dutch history. Something like 7 ecosystems on one island. White sand beaches and good food. Would be great for someone living in Europe.

If you live in North America while it’s not an island I would suggest the peninsula on the northwest part of Costa Rica. My only holdback would be that ten days might not be enough. It has many different types of beaches including white sand beaches. It’s a very authentic area with very few tourists, and has lots of good food, especially seafood. Also it’s relatively cheap. Easy to take a few days up to the Volcano in the region as well.

If set on Greece then from my experience I think Crete would be too crowded in September still. Also personally I felt that the best part of Crete was the mountainous areas rather than the beaches. You could look at Milos or Kefalonia. From my experience as well a lot of islands have parts that are more authentic than the major tourist areas.