Leros (Λέρος)
A fairly small island with not too many tourists, though this is changing as it becomes more popular. Accessible by air from Athens (it has a small airport) or Ferry from Kos, it is well worth a visit.
Leros is a really interesting island with some amazing 1930s architecture at Lakki, many neo-classical mansions at Platanos, and a massive castle, parts of which date from the 10th or 11th century. It is good for walking with most places of interest within an hour or so from the main Platanos/Panteli/Aghia Marina area. Excellent modern Greek food can be found in the tavernas at Pantelli and the island's people are very friendly.