Downtown Governor's Harbour has two or three streets of small independant shops where you can buy the usual souvenirs, plus great local art at reasonable prices.
Common items available for purchase include paintings of the local scenes, shells, and beautiful sarongs.
All prices are soft, so bargain hard! The Bahamian dollar is interchangable with the US dollar so no conversions are necessary.
Be sure and stop into the local bakery in the morning for amazing white brea and other pastries.