I think that usually when someone mentions the Caribbean they are referring to Caribbean Islands. If you are including the Caribbean side of Central America then I concur with kirbic's suggestion to go to Costa Rica. It has everything that you mentioned, lots of it, and at relatively low costs (although not as low as ten years ago).
For Caribbean islands I like St. Lucia. It is fairly mountainous including The Pitons, twin volcanic mountains on one of the coasts. It has numerous waterfalls and plenty of golf.
Thanks. All interesting suggestions, but yes, I think my wife had the Caribbean Islands in mind. St Lucia sounds good for that...We'll check them all out!
Went to the Caribbean for our honeymoon, many moons ago... saw
Trinidad
Grenada
Several of the islands in the Grenadines (too many to name)
St Vincent
Antigua
St Kitts
Nevis
Dominica
Barbados
Tobago
We saw St Lucia from St Vincent, and it looked beautiful from afar, and if we ever get back, it's top of the list of islands to go to.
From the list above, Nevis probably had the best golf coarse (at one of the resorts)... Antigua had a couple too. St Vincent was probably the best for waterfalls etc... though Grenada had a couple nices ones... as did Tobago. But... our favourite islands, by far were Young Island (quality of the resort... just off St Vincent) and Dominica (untouched wilderness... wonderful hikes).
All this reminiscing makes me want to drag out the albums from out trip.