I'll try to think of a place-it depends on what you want from a vacation. Is it mostly the beach, or is nightlife, culture etc also important? I'm in love with the island of Ikaria, but I don't know if September is the best time, weather-wise. I quite liked the island of Syros I went to last year, and it's definitely not pricey, but you need a car to get to the really nice beaches.

There are some lovely places inland too, and they tend to be cheaper than islands. Peloponese is lovely, though I need to ask around for more specific places. I'll get back to you.