Cuba!!!
Nobody mentioned Cuba: the BEST. We went there last year, rented a car for two weeks and drove from East to West all over the island. (arrived in Holguin and left from Varadero) The Cubans are wonderful people (it helps if you speak Spanish), every city has private ('dining room size') restaurants with excellent food, lots of culture and sun, and $1 mojitos. Cubans are very eager to speak with foreigners. Add the 1950's cars, some of the weirdest museums in the world, fantastic music scene.
I know that Americans aren't officially allowed to visit Cuba, but we met lots of Americans in Cuba, most of whom told us that they couldn't care less about that law, and they didn't expect any problems with the US authorities.