Downtown Nassau has excellent prices on liquor. Just don't get in over your head, you get to the point where the value of savings is outweighwed by the hassle of lugging it home! Even the airport in Nassau, with it's one dinky duty-free shop, has good prices on Absolute and the usual standards. I think we paid about $24 for two one-litre bottles of Mandarin (about $21 for one at home). If you like Nassau Royale (vanilla flavored rum), this is also the place. Prices are about the same in all the stores.
The best thing about liquor in Cozumel is that on the main drag there is a store that is the closest to a grocery store you will find. Along the back will is a giant refrigerator filled with just about every type of cold beer you could want. We were SO happy to find Coors Light, and HAL let us take it aboard no problem.