I raced last year in the Tobago International Cycling Classic and also in several races in Trinidad. Tobago was hot but less developed than Trinidad and thus better for training but there are many more local cyclists, shops and cycling teams with rides in Trinidad. Primarily in Port of Spain and San Fernando. There are cycling clubs and group rides throughout the islands of the caribbeans. Some places have better roads obviously than others. I've met racers from the former european colonies like Grenada, St. Kitts, Barbadoes, Curacao and Aruba who all sing praises of their training venues. Guyana also has a small cycling scene. Obviously road cycling itself is much more developed in the developed urban areas of South America, but I think it exists in very organized form throughout Central America too.
I've attempted to do some training in Costa Rica: It is hot in the spring and summer along the Pacific Coast - we found it almost prohibitively hot. However up in the mountains off the Pan-American Highway there are some spectacular MTB opportunities as well as road rides although the highway itself has truck traffic. San Jose is very crowded but there is considerable middle-class enthusiasm for road and mountain biking in the towns around the city. We saw hundred of yuppie cyclists on fancy carbon bikes training in the Orosi Valley on weekends. There was a beautiful paved road between Orosi and the Turrialba Volcanoe, where they trained. Costa Rica would definitely be a good place if you needed to do real training and not just adventure riding. Andre Brenes, for MTB world champion, has a shop in the town above Orosi.
That pretty much exhausts my knowledge of cycling in Central America and the Caribbean!