Prepare to haggle
Along the coast of Punta Cana, between the resorts, you'll find these little markets, with a group of local shops built of wood, where you can buy all kinds of Dominican souvenirs and crafts. The place I visited by the Playa El Cortecito, very close to my hotel. The Dominican store-keepers are very forward - as soon as they see you approaching, they begin to talk (hey friend! ... where are you from? ... Spanish, no? ... I have a cousin there ...) and will do everything short of using physical force to get you into their store. Inside you can find everything - sarongs, t-shirts with Dominican Republic logos, jewelry allegedly made from larimar or amber (actually plastic - you're better off going to a proper shop), key rings, small wooden pendants ... but the most abundant are the pictures, the "Taino art".