OK. This is one of those things where you just go to the place, there are no real addresses.
IMHO, the BEST of the various fishmonger-you choose it-they cook operators is the one at the S. end of the many, many places to choose from.
It has a HUGE over the water deck, some covered, some not. There are, on weekends, usually a couple of Mexican bands playing. On weekends. Esp. Sun. after church the place is filled with families and children. Calmest days seem to be Mon-Wed, especially for lunch.
When you enter, in front of you will be the cooking area. To your immediate right and left are different places to purchase food. But, what you want to do is go in, right past the central cooking area. You will come to a long refrigerated seafood counter where you will buy what is to be prepared as you like. To the right of the counter is a big refrigerated room where you can buy whole fish.
The key to being sure you are at the right place is that it seems to be the biggest concentration of variety under one roof (and it is the furthest south, toward Port's O'Call Village itself)
I usually buy shrimp, scallops and a variety of fish fillet's. You can choose from grilling, charbroiling, deep frying, etc. Options inc. vegetables, potatoes, garlic bread. ALL are good and are cooked on big, well seasoned grills.
Get lots of napkins, cold beer outside and have an orgy of food.