There are shops all over the town that sell black pearls. However, there are some shops that sell fake pearls made of glass or fiberglass as authentic black pearls, so beware. The best way to avoid being cheated by such shops is to look for authentication certificates at the entrance of the shops or refer to travel blogs and books for popular recommendations.
Les 3 Brasseurs is a must visit while in the town, since it is the only microbrewery in all of French Polynesia. However, be prepared to shell out a lot of money if you are drinking here.
Marche de Papeete is a great place to experience the vibrant local culture. On Sunday mornings, the market opens as early as 4 in the morning. Locals flood the place with locally grown fruits and vegetables, as well fresh seafood later in the day. Other than that, you can come rest of the week to buy jewelry, local handicrafts and trinkets.