Just got back from Thasos, a Greek island I had never heard of before arriving. Going in late May/early June, I found it at its best. It was a total change from any other Greek island I have visited: rural, beautiful, unspoilt and the friendliest locals I have met.
Ferries depart every one or two hours from Kavala on the mainland to Skala Prinos on the island and take one hour, 15 minutes. There are ferries from Keramoti on the mainland to Limenas (the island's main town) every hour or so in the summer, and these are quicker (and more direct) than the ferries from Kavala. Keramoti ferry port is a 15 minute taxi ride from Kavala airport.