Boca Chica  is not a choice place to do your shopping. Since the capital is so close, a day (or even an afternoon) in the Ciudad Colonial  would give you the best opportunity for perusing a better variety of keepsakes, and you’ll also find far better prices. Still, there are a few shops and stalls peppering the town along Calle Duarte, which runs directly parallel to the beach for about five or six blocks.
Here you can find rum, cigars, artwork (but it is the typical Haitian kind and not authentic Dominican artwork), clothes, and crafts. The prices in these shops are very high compared to Santo Domingo . However, if you just stay on the beach, the shopping vendors will come to you (barrage you is more like it) with briefcases filled with jewelry, women ready to braid your hair, massages, and various local arts and crafts.
Keep in mind that these vendors have hiked the prices way up expecting that there will be a healthy amount of haggling.