Hi robinho
I was in Rhodes last October. Bird highlights included honey buzzard, black kite, lesser kestral, alpine swift, crag martin, blue rock thrush, montagus harrier, redstart, winchat and hooded crow. I was there on a family holiday and not particularly for birding so I am sure there is alot I missed. The Acropolis at Lindos, an unlikely birding place, was really good for alpine swifts. The acropolis is high on rocks overlooking the sea, a most spectacular place, and the alpine swifts were supurb there flying right around our heads, you could almost touch them. It was one of those magical birding moments for me. Another good place were the beaches in the southeast. It was sort of marshy getting there and there were loads of winchats and that is also where I saw the montagus harrier. I'm sure with more time I would have seen more. You are going in June so it will undoubtedly be different than Oct.
Have a good time.