colonial zone
The Colonial Zone offers plenty of shopping opportunities, especially if you are looking for Ambar and Larimar, the traditional stones of the DR. Don't forget to haggle, as all the shop owners adjust their prices for this purpose. You will also find a ton of Haitian art for sale everywhere at great prices. If that's your thing, great, just remember its not Dominican. The main boulevard in the Colonial Zone is El Conde, a pedestrian boulevard lined with all kinds of shops and eateries mostly aimed at the locales. Have fun shopping and people watching here.
If you are feeling adventurous, have a cab take you to the Mercado Modelo nearby. This indoor labyrinth of shops can be overwhelming for a new tourist but, don't worry, it is safe. Then again, you might feel safer asking the cab driver to escort you through the maze of shops and kiosks offering every imaginable kind of souvenir, jewelry, stone, artwork, etc.
malls
If you want to experience American-style shopping there are plenty of options but here are the three most popular: Plaza Central, Acropolis Center and, for those of you willing to venture into Santo Domingo Oriental, MegaCentro. Remember: no haggling at the malls. While MegaCentro is farther away than the others, it is the second largest mall in the Caribbean after Plaza Las Americas in Puerto Rico and is a destination in and of itself. This place is HUGE!
Please remember when shopping at the malls, this is an island where practically everything being sold is imported and, worse yet, taxed at 16% ITBIS or Value Added Tax. Don't expect to find too many bargains to brag about back home!