Try Jamaica - it has all you could need and more. Plenty of sun, sea, sand, culture, stunning scenery, beaches that go on for ever, exotic scenery, rivers, mountains, waterfalls, snorkelling, diving, eating, drinking, music, fun - spent two weeks in Negril last May - spent some time on the beach - well there is 7 miles of it, there are also cliffside hotels if you are not too mad on the beach, losts of little interesting hotels intimate resorts as well as massive and not very personal all inclusive places. I think it's pretty crazy in the winter as it's high season. Try Treasure Beach which is similar to Negril but a bit quieter on the south coast of Jamaica. It doesn't cost much to ask a taxi driver that you like to take you out for the day and bring you around. the food is lovely, the sea is amazing, the sunsets are like you have never seen. I just want to go back!!! will have to save up a bit of money first.
I hope you find what you are looking for anyway. Oh yeah - avoid Montego Bay - sounds very exotic but it's not.