I am halfway through my 2 week Cyclades island hopping holiday. The third stop is Naxos, which is the biggest island of this island group. Naxos does not have a port for cruise ships, the airport is also limited to what of tourist can come in, but that means you will not find mass tourism here.
Naxos: if I win the lotery, I will move back to Greece and find myself a nice place to live somewhere on your west coast ;).
Read part 3 of my Cycladic adventure.