I agree with the idea of Naxos. It is a big and wonderful island with diverse landscapes (In May we like hiking there !) . If you rent a car you'll see the different coasts and it is worth it. Naxos is connected by air or sea with a lot of destinations.
Moreover Naxos is connected by boats with Delos
and Delos is, with Delphes, one of the most interesting archeological site in Greece
(to my opinion). Naxos is very near from Naoussa on Paros island, and everybody loves the small fishing
port of Naoussa !
Two years ago we spent one week in Naxos, last years 4 days and we continue to love it.
It will be a very attractive and convenient choice.
But, if you have time to sail to Turkey, there is another choice I wrote about : Sporades islands. When we sailed from Corsica
to Turkey 6 years ago, we did this trip by Kalkis bridge and visited most of the Sporades till Thassos (the northern Greek island in Aegean see) and then south (with the wind
in the good way - northerlies - to Kusadasi. We did it again 3 years ago (I mean a "circle" from Kusadasi to Kusadasi where Metis is wintering...If you think you will visit Cyclades later, it is a wonderful sail trip, less touristic, more authentic, more green, aso...