St. Lucia has fantastic Rum Punch. It's hard to go wrong. Highly recommended:
Chairman's Reserve cask-aged dark rum
Crystal Lime clear rum infused with lime
Most bars will have both, even at the smaller resorts.
In addition to rums, Piton Lager beer is brewed and bottled on the island and is quite good although it has a slightly higher alcohol content than most American beers. It's usually offered in eight ounce bottles, often for $1 US.
Also seen in coolers: Heineken, Champagne, Wine, Water, Coke usually $1 US
