Most hotels have at least a small souvenir shop. However, much of the merchandise is overpriced. If you're looking for a bit of a bargain and are not feeling going to the Straw Market in Nassau, there is a little straw market located on the other side of the strip. It doesn't have as much variety as the one in downtown Nassau, but it is something nice to do to and you can find nice cheap gifts. Further located in Cable beach are more shopping plazas with liquor stores, some clothing shops and fast food restaurant.
Also, along the beaches, there are people selling cigars, shirts, and jewelery which are very authentic and unique in the Bahamas.