Just done a quick search (bored of revising).
Olu Deniz, where many people have recommended on here as well as myself, is more than within your budget.
Dozens of hotels for 10 nights, all inclusive, with flights, for around £500-£600 per person going for 10 nights (20th-30th July).
Oh, and...
Another vote for Olu Deniz or Hisaronu.
Stayed in Ovacik, about 3/4km away from Olu Deniz (1/2km from the town of Hisaronu) and felt it was a bit far out having last year stayed in Hisaronu itself, felt much closer to everything. Loads to do in the day for next to nothing in comparison to other...