You're unlikely to find any decent Caribbean that far north in the state. If you are open to somewhere that reflects local flavor, I would suggest a visit to the Saltwater Cowboy in St. Augustine beach:

http://www.saltwatercowboys.com/

Located in a rustic building overlooking a intercoastal river, this has always been a favorite of mine and serves fresh, quality seafood, as well as other regional "delicacies" (if you're open to trying gator tail, this would be your place--not my sort of thing!). This place doesn't take reservations, however, and patrons start to queue at 5. Worth the wait, however.

There is also a very modest place in the historic district, the Spanish Bakery, that serves fresh bread and surprisingly good and inexpensive Spanish-style lunch in a casual setting. Also worth trying if you don't mind eating outside on a picnic table.

Others might suggest the Gypsy Cab Company; I haven't found the food or service there to be anything more than mediocre.

Enjoy your visit!