£2k each or for both of you??
If it is £2k for both that money probably wont stretch to private villa type accomodation, unless you look at Thailand, Bali perhaps.
Weather wise, Turkey, Morrocco, Egypt, Tunisia will be nice, not mega hot but very warm, nice sea temperature and little rainfall. Some of the resorts are excellent and although they may not feature exclusive beaches and private villa's £2k will get you a 5 star all inc resort with the hotel's private beach and excellent facilities.
The Caribbean will be entering their "Rainy" season. That said, because it is a tropical climate, when it is hot, it is still very hot and it only tends to rain in short sharp bursts meaning most days will be largely dry with partial cloud.
£2k will go a long way in Cuba, a wide range of all inc resorts
Looking at Europe, Greece is always a good shout with massive choice and many Greek destinations would provide you with nightlife and quiet day time relaxing too. As you are travelling just outside the peak time, your money will go a long way. £2k will get you an excellent hotel, with the exclusivity you may desire.