The International Bazaar is one place to go. You can find island made handcrafts (bongs a plenty, steel drums, wood carvings, etc) and you can find your basic souvenirs. There is a lot to do and see in this area and you could easily spend an afternoon here.
As of June 2009 The International Bazaar is pretty much dead, just a handful of stores is open, nobody is there, walking around the place is depressing but perhaps somewhat educational as to what damage a hurricane (I think it was Wilma) can do. Structures are damaged, broken, looked quite dangerous. Do not waste your time, not until they re-build which I didn't see happenning. Two big hotels and casino around the bazaar are damaged and closed as well.
The International Bazaar opened in 1967 and was designed by a motion picture special effects expert from California. It is a 10-acre complex divided into sections representing different parts of the world and has 90 Shops, 13 Restaurants, and 6 Snack/ice Cream Stores in it.
On January 1, 1992, the Government of the Commonwealth of The Bahamas abolished import duties on 11 categories of items (Perfumes and Fragrances, Crystal, Leather Goods, Jewelry, Fine Linens and Tablecloths, Watches and Clocks, Photographic Equipment, China, Binoculars, and Telescopes). You can find saving of between 25% - 50% below US prices on many of these items.
Even if you aren't a shopper, this is a nice area to stroll around through and enjoy the flower covered brightly painted buildings and cool air conditioned shops. You may even be lucky enough to be there when an outdoor band is playing by one of the restuarants, like we were.