The Bahama Grill is a colorful, two-story BBQ joint at Saunders Beach—west of downtown, just past Arawak Cay. It offers ample portions of inexpensive, excellent hickory smoked pork, baby back and beef ribs, chicken (rotisserie, grilled, or barbecued), burgers, and seafood (grilled fish, lobster, shrimp, fritter-like conch balls, and conch burgers). 
You can dine in the modern, light-filled rooms all done in bright primary colors or on the outdoor deck. They do a roaring local take-out business, so be patient waiting for your order. It will (eventually) arrive. Upstairs is a funky little lounge for cocktails.