Cyprus gets my vote.
Good weather in September,
lots of history and places to visit, very easy driving there so you could hire a car and visit all the sites and see an awful lot of the island in the process. Great food and great people and only a 4/5 hour flight time from the UK.
Friends of ours asked the same question some time ago and plumped for Paphos, they went last month and had a great time. They went for 2 weeks and visited many historical sites in their hire car and then to break the fortnight up they booked a 3 night stay in the East of the island, they enjoyed the change of scenery and visited lots of sites on the drive there and back and enjoyed the beaches too, along with seeing Nicosia, Larnaca and Famagusta.