There are several shops near the port that have good prices on rum. About half of what you'd pay at home. Trip is right though, Appleton's is the best rum in Jamaica and arguably the world. Try some of their aged rum, it's super smooth. I can't remember but I think it's two litres per person limit.
yup appleton..you can get it on the ship also...not much difference in prices I am such NOT drinker that i still have 3 bottles we bought in 1993,. they came in pretty tin cans lol. We brought 10 home and gave a few away, so you can see we dont partake often huh?