I come from a southern family who makes a lot of southern food and this is the best I've ever had. In my opinion, this is the most important thing you can do in Savannah. Do one of their famous bus tours. Pick up some pralines down by the river.
In Hilton Head, Skull Creek Boathouse and The Old Fort Pub. Make reservations at The Old Fort Pub during the sunset, it's breath-taking. Golf in H.H. if that's your thing. For an affordable, but excellent course, try any of the courses at Palmetto Dunes. The Robert Trent Jones is my fave. If no golf, go to Harbor Town and rent bikes and ride around. Looking at the alligators is fun if you've never seen them.
In NOLA, the restaurant list is to long to discuss, but one of my faves is the Napoleon House. Plantation tours can be fun, particularly Oak Alley.