there are a "few" liquor stores is Key West - first there is one called Lost Weekend Liquor Store at 427 Caroline Street - phone number 305-296-4545 which is only about 2 blocks from Mallory Square, then there is Key West Liquor which is located at 705 Duval Street which is 7 blocks from Mallory Square and their phone number is 305-294-9874 - I know Fausto's Market carries wine and beer, but I don't know if they carry liquor - Fausto's is located on the corner of Bahama Lane and Fleming Street which is located in front of Fast Buck Freddies and the ol's Hotel La Concha --if you "shop" at the the different bars, its going to be pricey -----If you can get to the blvd, you will find a Winn Dixie located at 2760 North Roosevelt Blvd and their phone number is 305-294-3664.
Hope that this will help.
Always]
Shirley