Check out what the ships sells. Usually the prices are good, as you don't pay the extra tax. Just look for your favorite brand.
On the islands, you can ask the shop keeper what he recommends. Often, there is a local made brand. I am not sure if that is true of the Bahamas, but other islands have their local brands. (Jamaican rum in Jamcaia, Puerto Rican rum in Puerto Rico)
I also like to buy vanilla, hot sauces, etc. Those are always very good! Costa Rica and Jamaica has great coffee you can buy also. Grand Cayman also sells Jamaican coffee.
Equal opportunity cruiser since 1998-4 Carnival, 4 RCI, 3 HAL, 3 Princess, 4 Celebrity, 3 NCL, 1 Disney
I have now achieved-
ONE HUNDRED DAYS ON A CRUISE SHIP!!!!!!!!!!
139 days total