What is a fun tropical place to visit thats not more than like 5 hours from New York.?

By air, or by driving?

By air, I would recommend Paradise Island in the Bahamas (The Atlantis Resort is awesome).

Driving wise - You don't have much by the way of tropical locales. I prefer the Wildwoods in the Jersey shore for my beach type vacations. Family oriented in wildwood Crest, a little more hopping in wildwood. Great Boardwalk and plenty of good restaurants.

any place in the caribbean or the bahamas - I think it's 3-4 hours away?

Caribbean Islands. There's a lot of choice, see below

Look downtown at Harlem. I hear it's a jungle down there.