Hi there! I have lived and kitesurfed in Rhodes for 12 years - now it is sunny England for me, tomorrow Hustanton for the first time with a Cabrinha 2006 I borrowed from a friend, haha, never mind... Here is some info you need:
West coast spots / schools:
Kremasti has side or side-on wind, the school name is Air Riders, google it for further info. Generally pretty windy in August unless you are unucky, best wind between 13:00 and 18:00. It is 5-10 min drive from big hotels in Ixia (Rhodos Palace, Olympic etc), another 10 minutes if you stay in Rhodes town. Nice people, manager Dora.
has another kite school, similar wind timing, direction and intensity, another ten minutes to reach it from Kremasti. Nice people there as well, manager Spyros. Doretta beach hotel just next to the school.
Fanes has another kiteschool, 5-10 minutes from Theologos.
Prasonisi is an incredible spot. Wind almost guaranteed for August. Waves (but on shore, must have your upwind sorted out) and flat (but side-off shore, must be careful not to lose your kit, better buy rescue before you need it, it is cheaper unless you are a pro in self rescue) on the same spot. There are two kiteschools and 2-3 hotels, also restaurants. If you haven't booked early you will not find accommodation there. Look a the map for nearby villages and resorts, you must look on the East coast in places like Kiotari, Gennadi, Lachania, Plimmiri or if you are prepared to drive a bit longer, Pefkos or Lindos.
Food and wine available everywhere on the island. No worries there