Kayaköy, or Levissi as it was known to its former inhabitants, was a Greek town until 1923, when, after the multinational Ottoman Empire drew to close, governments of Greece and Turkey concluded on a population exchange to become nation states ethnically homogenous as much as possible on the basis of Treaty of Lausanne.
The ghost town of Kayaköy itself, including hundreds of abandoned houses with no roofs or windows, and the walls of some of which are partially ruined, is the main sight. Those not to be missed include the old fountain which dates back to 1888 by the tarmac road, two abandoned churches (aptly dubbed Yukarı Kilise and Aşağı Kilise, i.e. “Upper” and “Lower Church”, respectively, because of their relative elevation difference to each other), and the little chapel on the top of the hill (about 20 min uphill walk from the lower church; follow the red dots from the church), which gives a stunning view of the valley and the sea below, which are located on the other side of the hill that Kayaköy leans against, and therefore is not visible from the town itself.
The lower church and the streets (or stairs to be more precisely) in its vicinity has been declared a “museum” by the Turkish Ministry of Culture with a ticket office in the entrance which require anyone passing through—whether they have the intention to check out the church or not—to buy a ticket which costs 8 TL pp. You may pass on the early and late hours of the day on which the office is unmanned without buying a ticket, though.
Text from Wikitravel, Kayaköy