Remeber this is the tropics. Most of the island is surrounded by coral reefs so from the shoreline you really don't have access to the open ocean.
If fishing from the shore you are thinking of surf-fishing for bluefish off the beaches of the outer banks of North Carolina. You will not get that here.
Most fishing is done in deep-sea or over the reefs themselves. If you want to catch big snapper or grouper you will need to find deep reefs located a bit off shore, if pelagics is what you want, plenty of tuna, mackeral, Dolphin(dorado), Wahoo. Also the big action for Sailfish and Marlin is plentyful.
On some rivers you will find Snook and Tapon it all depends on the area of the country you will be in.