There's enough of a savings over U.S. prices (30%-50%, in many cases) to make duty-free shopping profitable on New Providence and Grand Bahama. On all the islands, be sure to visit the straw markets, where you can bargain for low-price hats, baskets, place mats, T-shirts, and other items. But be aware that most of the straw goods you find in a straw market are actually imported from Taiwan or other places. Remember also that duty-free means that the shop doesn't have to pay taxes, not that you don't: if your purchases exceed your exemption -- in most cases, $800 per person for U.S. residents -- you'll be liable for duty when you go through customs at home.
For authentic souvenirs, check out the art and crafts galleries you will find throughout the Bahamas. Most are concentrated in Nassau. Bahamian artists hold their own in the burgeoning marketplace for Caribbean art.
Trademark products include Junkanoo-inspired art, wood sculpture, painted straw masks, handmade batik, model ships, and hand-plaited straw work. Jackson Burnside is one master of Junkanoo art. His Doongalik Studios in Nassau sells his work and that of other artists.
Long Island is known for its hand-plaiting, which has survived the onslaught of cheap imported goods. The island of Andros is home to the Androsia Batik factory, which produces island-style batik cloth and clothing that is available throughout the islands.
On the island of Green Turtle Cay, the Lowe brothers are famous. Albert Lowe is the official Bahamian artist, whose masterpieces dwell in the four- and five-figure price range. Vertram Lowe assembles realistic models of sailing ships, which start around $700.
In Providenciales in the Turks and Caicos, Bamboo Gallery carries fine local, Haitian, and other Caribbean sculpture and paintings. You can contribute to the well-being of the islands' environment by taking home handmade crafts that don't include such natural items as coral, feathers, and rare shells.
U.S. Customs does not allow any product made from black coral or tortoise shell into the country. Smoke your Cuban cigars in the Bahamas. They're illegal in the United States, and the fine is stiff.