Limnos or Lemnos (Λήμνος)
Not an immediately picturesque island but it grows on you; after a few days we didn't want to leave.
Limnos has good beaches, some very significant archaeological sites, and not many tourists. The main town of Myrina has a a lot going for it too, with a splendid castle, a nice harbour and some excellent tavernas. The food here is among the best we have had in Greece.
