You might want to look at Chora in Andros. Andros is the most northern of the Cycladic islands and you can get there via the port of Rafina which is a half hour bus ride from the airport.
We visit often and have written up our view of it
It's a quiet little town on a headland with mainly Greek visitors. Two beaches, one of which has a road and a few cafes behind and the other of which is completely undeveloped. Good walking and a handful of nice eating places.
We always stay at Karaoulanis rooms run by a nice Greek / French family. (Full disclosure, we've become quite friendly with Yannis and Caroline.)
There are other options down by the beach if you don't fancy these.
Andros certainly fits the bill as quiet and relaxing and it isn't the kind of place you are going to get any hassle as a single woman. It's very local and family oriented.