with that budget, i'd recommend turks and caicos. my wife and i went there (providenciales) last may and it's our favorite caribbean island we've been to. it's simply amazing with the most beautiful beaches i've ever seen. we rented a car and drove all over and went to some very secluded beaches. there isn't too much of a nightlife there though if that is what you were looking for. but it's very relaxing and laid back with some of the best food i've ever eaten, with many restaurants literally on the beach. if we weren't having our first kid in 3 months, we'd already have another trip planned to go back there.
personally, i do not like all inclusive. i've done it once in costa rica and most likely won't do it again. when i'm on vacation in another country that i may never go back to, i don't want to be couped up in 1 spot the whole time i'm there. we like to explore.
although, we did go to the atlantis in the bahamas, and while we did not explore the island that much while we were there, we LOVED that place and the atlantis is so huge that you can not even see all of it after 4-5 days. i'd love to go back to that place but we just haven't made it around to there and have wanted to go to other places.
i've been to cancun (2x), barbados, bahamas, aruba (2x), and costa rica. also the florida keys are very nice too, but not quite in the carribean. while not in the carribean, we went to maui on our honey moon and that place is also incredible.
cancun is way more party, and a shitload of fun if that is what you are looking for. i also found it relatively cheap in general, especially compared to other places i've been.
EDIT:
this is taylor bay in turks and caicos.
so secluded and beautiful. there were about 6 people on the whole beach the whole time we were there. and that house on the tip there is dick clarks old house lol.