Gavdos is a tiny island in the Lybian Sea, just an hour and half of ferry from Crete South coastal village of Hora Sfakion (or Sfakia). Apart from August, when the island can be quite crowded, you can enjoy the feeling of being away from the world (or not necessarily too far away, it's up to you).
From the port you can get a lift to Korfos, where an easy path leads to Tripiti in an hour walk. In Korfos there are a pair of good tavernas where nice and clean rooms can be rented, but my wife and I, we spent a week on the Tripiti pebbly beach with our tent, only coming back to Korfos when we need to refill our water tank or to enjoy the local food, sitting in a taverna porch. It was September, the days were very hot, but the nights were incredible: fresh with a sky full of stars, the silence complete, only the sound of the waves.
But you don't need to be so naive; staying in Korfos (where there is a nice little beach) and going sometimes to Tripiti is a good experience.
Yet, when the last daily tourist (if there were someone) has gone, the beach and the cape are your, till next day. It's a unique experience. And consider that you don't need a lot of camping gear, a sleeping bag, some water and tinned food are enough. Don't be afraid to be alone, there isn't any danger at all, apart that ones that you can provoke: don't light fires!
With a fifteen minutes walk along the beach and then on a path over the rocks, you can get the big concrete chair just over the cape: climb over it and enjoy the sight!
From Hania (where you can arrive by plane) there is a bus service to Sfakia, where the ferry sets off to Gavdos.
Looking at www.sfakia-crete.com/sfakia-crete/ferries.html you will find the ferry timetable for Gavdos as long as bus timetable for Hania-Sfakia service. Hania is the nearest international airport.
Sarakiniko is the Gavdos main hamlet, with a good choice of domata (rooms) to rent, tavernas and a wide sand beach. There is a supermarket, too.
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