Rhodes is very nice destination for kitesurfing. I was there last September for 10 days. 4 nice days, than it turned from the North and got to 17- 20 m/s, after nothing. You can definitely kitesurf close to the Rhodes city but the beaches which are open to Melteni is stony. And there will be a lot of tourists in summer.
We stayed in Fanes which is 30 km from Rhodes city and just 15 km from Rhodes airport. Austrian guy Semy organizes kitesurfing summercamp there and they are based in hotel Delfini (we paid 30 EUR per room). I think this summer it will take place the fifth time. Kite surfers are mostly Austrians, but could be from Holland and Germany.
Sandy beach, just over the hotel's garden. Not wide, just 20 m but very lonely. You will find more details here
http://www.airtime.f2s.com/html/index2.html
Place is nice and if you want to enjoy real Greek food (food cooked for Greeks) and cheap uzo just walk to Fanes. It is 2 km from the beach. No tourists. Package tourist hotels are concentrated from Rhodes city to the airport.
During summer months Rhodes gets Melteni and it comes from NW (side- onshore). In September there could be very strong winds and direction more from N (onshore). It is not Melteni, is called differently. In summer Melteni rules!
Prasonisi (the most southern point of Rhodes island) gets much stronger Melteni than in places close to Rhodes city which is the most Northern part of the island. Prasonisi is not a place for beginners. Wind on southern beaches should be offshore.