I find the best prices in A.H Riise (sp?). They have a location in the mall at the port in St.. Thomas and if you want, they will deliver it to the ship, but you must purchase it 3 hrs prior to sailing. I have made this my first stop in St. Thomas the 4 times I have been and have never had a problem with it being delivered or receiving the wrong bottles.
I find the best place is the liquor store around the corner from my house. This way I spend none of my vacation time shopping for something I can buy locally. I have no worries about getting something delivered to my room and do not have to shlep liquor bottles around on taxis, planes, through airports and such. Personal choice, the savings is not worth the time and effort on my vacation time.
I can't speak to St. Maarten, but the place in St. Thomas is NOT the A.H. Riise stores. The prices are slightly cheaper at a store right at the wharf where your ship comes in, but I can't remember the name of it. A.H. Riise also has a store at the wharf, but this isn't what I'm talking about. At the wharf you'll find small pedestrian-type streets extending away from the water in a shopping area (you'll know it when you see it) and the store I'm thinking of is pretty close to the water-side of one of those streets (i.e., not at the far end of the street). The name might be Century or Paradise (?) or some other word-type name, not a "person's" name.
Prices on vodka and liquers are excellent. Prices on single malt Scotches are not very good. The fabulous prices are on rum and Kahlua.
I agree with Dell that St. Maarten is incredibly cheap for liquor. I was there in January and brought home a litre of Courvoisier VSOP Cognac for my dad at $18.95. It is at least $40-50 at home. Prices are so cheap that you can go kind of crazy.
I don't remember names, but it only takes about 1/2 an hr. to walk along Front Street to the end of the shopping area and then wend your way back, checking out prices. Beer in convenience stores our from "ice cream carts" is as little as 50 cents a can, and you can enjoy it while walking along. It is correct that prices drop further along the street, but I don't think any of the prices end up being radically different. Back Street, one street over, is where the Islanders shop, and there are good prices there too, but on things like shoes and clothes, not so much expensive jewelry or other consumer goods. Many jewelry stores sell liquor too! While looking at jewelry in one store, Ray's, we were plied with champagne and Heineken's, not to befuddle us, but being hospitable. We were not on a cruise ship that vacation, and the staff said because there were none in town they would just cut the **ll**it and gave us their rock-bottom prices on their goods, without haggling. This was very refreshing, and their prices did seem to reflect the kind of prices you could get by dickering..
Do save all your shopping $$ for St. Maarten, you won't regret it.
Last time I bought booze on an island it wasn't delivered to the ship! It took 3 months to get a refund (which was converted from Cayman $, so we lost a little in the conversion). What bothered me most was that it was all for gifts! Try to find something on the last day of the cruise in the shops on the ship so I wouldn't come home empty handed! Now I only buy ON the ship. That way, I know it's coming home with me or I will be credited immediately. The prices weren't bad ($10 for Kahlua, $24 locally) Absolut was approximately the same price.