Hit Market Street. Pearlz Oyster bar at Happy Hour is a must. Great Oysters at a very good price then (about $10 or less a dozen) and half price craft beers. Just up the street is Magnolia Cafe for dinner or lunch. Amazing modern southern food. They have this appetizer, that makes a great lunch, its chicken livers sauteeded in cognac with country ham, and damn its good! Shrimp and grits, she crab soup and the whole nine yards. SNOB (slightly north of broad) is good too and in the same vein though a bit more upscale, as is Rue de Jean, if you want farmhouse country French faire. My advice is to buy anything involving a dead sheep or rabbit there. Its a great food town. Have fun.
PS if you like tea, they have a tea plantation locally there, the only one in the US, and their breakfast tea kicks ass. I didn't take the tour, but I did buy a few boxes. It was about the best I'd had as it was fresh and hadn't sat in a warehouse for months.