There are many trinket shops in Sosúa [1], but for a nice art shop go to Viva (Calle Dr. Alejo Martínez, tel. 809/571-2581). It has a wonderful selection of local art and Dominican paintings. It is a good place to buy a traditional Dominican craft gift for someone back home.
Patrick’s Silversmithy (Calle Pedro Clisante 9, tel. 809/571-2121) has interesting larimar, amber, and coral jewelry pieces that are affordable and unique.
Shopping along Playa Sosúa [2], you’ll be able to find all the regular trinkets in a long line of booths. Haggle your head off for T-shirts, sunglasses, jewelry, and paintings and you’ll hopefully get a good deal. Shopping like this might get a little tiresome, while being hounded by all the hawkers trying to get you to buy their lookalike wares, but it is an adventure, and you don’t have to leave the beach.
Links:
[1] http://www.moon.com/destinations/dominican-republic/the-north-coast/sosua
[2] http://www.moon.com/destinations/dominican-republic/the-north-coast/sosua/sights/beaches