Spent a week in Cyprus a few years back. We stayed in Limassol which turned out to be a bit of a **hole - flatwater though. We went in Feb. where the coastal temps were in the 20's. A couple of hours drive up into the Troodos Mountains and it was snowing, so if there's no kiting, grab a snowboard and head for the hills, but I guess it'll be summer/autumn when you're there, so maybe stick with the kiting.
I went to Cyprus to kitesurf last year. I was too late in the season. You are going at the best time as the seabreeze kicks in about May/June to Sept/Oct (15 - 25 knots). You are also going to the right coastline to catch those seabreezes but there is also some good kiting on the other side.
There is a good beach a couple of kms south of Larnaca (sorry I can't remember the name - might be Mackenzie) but the website suggested will give you all the info you need).
There is a great beach on a seabreeze between Pafos and Limissol called Paramali Beach which is near to Pissouri Bay. You need to drive into private property though and park in the olive grove. Everyone needs to be careful not to ruin the olive trees as they face eviction if damage is done. The beach is a pebble beach so even though they are mostly smooth pebbles it's an idea to take booties.
The Authorities in Lanarca are pretty strict about how close you can come into shore and will take you off the beach if you get too close to swimmers.