I went to Kefalos Kitesurfing a few years ago and it was a great spot. Not much to do on the beach but Kefalos town is only 5 or 10 minutes drive away and has loads of places to stay. Also lots of variety of places to eat but not too commercialised. The wind is pretty much on shore (Kefalos kitesurfing is on the North of the Island Kefalos town is on the south and more famous for windsurfing as it has offshore winds) and water shallow for quite a long way out. They were a bit reluctant to hire kit for free riding unless they were convinced you knew what you were doing, so you can either take your own kit, have a quick hours lesson or take you album of action photos to show them!!!
It's always difficult to recommend a place to people as everyone looks for something different but I think Kos is a great place as long as you have a car as there is enough variety there to please everyone.
The Kefalos Kitesurfing web site isn't all that so doesn't give a good impression I think that it is also called Kohilari Beach kitesurfing too so may be worth having a trawl of the web. Let me know if you want any more info
Paul