Port Lucaya Marketplace is a good place to do your souvenir shopping.  You can start with the straw markets where the vendors have everything from jewelry to dresses and many things in between.  Never take the first price they quote you.   They will definitely bargain with you and always check the next shop around the corner, where you might get an even better deal.  There are many restaurants, alcohol stores and clothing and jewelry shops in the Marketplace, too.