Amorgos

Amorgos is the easternmost islands of the Cyclades. It is a fairly mountainous island of the Cyclades and invites more for walking than for swimming, although there are beautiful beaches.
Amorgos was in the 90s famous from the movie "The Big Blue," which plays partly on the island.
There are two seaports on Amorgos, Aigialis and Katapola, from which Katapola is the much more attractive. In Katapola there are a lot more restaurants, bistros and accommodations. Another advantage is that most ferries arrive here.