On East Bay street, just east of the Paradise island bridge (Mackey st) there is an exquisite Bahamian restaurant. It's an old pastel-colored colonial house with manicured grounds and a beautiful porch . I had probably the best grilled conch I've ever had there. Expensive, but not unreasonable. If you want to try the best in Bahamian and carribiean cuisine, give it a shot.
To the west, within easy walking distance of the wharf, (I think on Marlborough street) is a good cheap place to get fried conch, fritters and Bahamian food samplers. I forget the name of the place, but it's easy to find. You really can't miss it if you walk west from the wharf.
Right under the Paradise island bridge (Mackey street) is a food market where you can get the most wonderful fresh conch salad and seviche right from the stalls. Not really dinner but a great place to stop by if you're wondering around. The conch is still alive when they cut it up for you.
If you have a car, on West street (straight up from Junkanoo beach) there is a 'local fare' restaurant that serves up great and inexpensive Bahamian food. This is the place to try souse, pig feet, skillygalee, duffs and the like. If you want to experience what the locals eat, this is it. Flavored duffs are a must here. Any hotel concierge can direct you, or just drive up west street and look to your left.