Well, they're all southern, since it's below the Mason-Dixon line :D. Do you mean traditional Charleston desserts? All of the nicer places will change their dessert menus daily. Where are you planning to eat?
The coconut cake at Peninsula Grill is famous. I like it fine.See if Hominy Grill has Hummingbird cake. If you see Huguenot Torte anywhere get that. Those are the traditional ones. Pecan pie at Page's in Mt P is outstanding.