I travelled to this amazing island next to Turkey for a short holiday; and I strongly recommend to visit it.
In my opinion, the best time to go there is not in summer. Many people travel there during that time, but if you don't love crowded beaches and high prices, you'd better choose another season. I travelled there in winter, it was almost spring time, and the weather was pretty good.
In that time of the year prices were lower, food was delicious and local people were very friendly.
The flight was cheap and the plane very comfortable, with a lot of free sits.
If you have never been to this almost unknown country, next to Turkey, why don't you give it a try?