Every hotel has a bar and there are lots of little bars and restaurants around. But drinking in bars in French Polynesia is damn expensive. Your best bet is to buy some Hinano bombers at the store and drink on the beach.
You will be charged an additional 60XPF deposit fee when purchasing Hinano bottles larger than 12oz. You can redeem your deposit at any location that sells Hinano. The larger bottles are sent back to the Hinano brewery for reuse/refill.
Tabu is another local beer, only available in 12oz bottles and slightly more expensive compared to a 12oz bottle of Hinano. Tabu is better tempered to the Tahitian heat. Unlike Hinano, Tabu is very drinkable at all temperatures: cold, slightly chilled, or room temperature.