Most probably you have never heard of such island but it does exist and it has permanent residents as well. Its small size (43 sq.km) and its remote location in the middle of the North Aegean sea keep mass tourism away and the island has preserved its slow-pace and isolated lifestyle. Also, Agios Efstratios (called Ai Statis in short) used to be one of the places where Greek political prisons were sent in exile, including the famous musician Mikis Theodorakis.
The closest island to Agios Efstratios is Limnos, and both are connected via ferry from the port of Kavala a few times weekly, as the trip takes about 1.5 hours from Lemnos and 6.5 hours from Kavala. Ferry connections are also available with the port of Lavrio (7.5 hours) which also stops at Mesta on Chios island (5 hours). Please note that these ferries may not run everyday even in the summer so there may be days in which you cannot go to or leave Agios Efstratios. This island is suitable for those who want not only to enjoy quiet holidays but also to taste life on authentic North Aegean island, not influenced by tourists in any way. Hikers would find it perfect.
There is only village with the same name - Agios Efstratios, and all houses and public facilities are to be found there. Accommodation is limited and provided in rooms and apartments to rent or small holiday homes. A few restaurants serving local dishes, cafes and mini markets are available as well, everything within the village limits. The rest of the island is totally undeveloped, although it is crossed all over by unpaved roads, with rocky hills and small valleys, covered by low vegetation and grass. The beaches of Agios Efstratios are of volcanic origin and they are rather pebbly and with coarse grey sand. The coastline is rich in geological formations and sea caves which can be best seen by boat. The only organized beach is right beside the port, long sandy beach with shallow water, which provides sunbeds and parasols in the summer. The rest beaches on the island are accessible via dirt road or on foot (and as you can properly suggest they are empty most of the time), others can be reached only by boat. The most famous are Alonitsi on the northeast coast and Agios Dimitiros and Ftelio on the west coast. The friendly locals will help you with instructions for any place you would like to visit on the island.