The main shopping area is the village of Vaitape. However, I did not really buy anything there, and found shops along the main road outside Vaitape(I can't say off the beaten path because on BB there is only one "path"!).I bought great Gauguin pareos (huge!) at the Boutique Gauguin. You can't miss it , the giant cutout of Gauguin screams tourist trap, but I couldn't resist and did end up buying artsy souvenirs, including tapa cloth,small woodcarvings, and those great batiks of Gauguin paintings (not made on BB, but who cares). I also recall buying local fabric at a shop nearby along the same road, cheaper than in Vaitape.
All around the island you will find little shops where you can buy the local sarong, called pareo in Polynesia. They come in different bright colours and are easy to wear.
You will find so many beautiful pareos. They can be worn so many different ways, on men and women. You can use the as table cloths or wall hangings too.