Jamaica is in that price range.. try SAndals Grande Riveria (I believed it used to be Sandals Ocho Rios).. Been there years ago and the food is great.
Also Dreams Punta Cana (the more expensive one) is damn good. The food is to die for.. all you can eat Cuban Lobsters at the buffet twice a week.
If you can hold off till Hurricane season, it's 65% off. Got a room with a butler at Sandals Bahamian. I believe it was a bit more than your budget but it was originally price $12,000 + ... but they have Gordons on the Pier and this other restaurant that is free with Butler package. The rock lobster tail .. OMFG!.. You have to pay if you don't have the butler package though.. There's other non-paying restaurants onsite too.