Sounds like quite the trip. I'm jealous. I've been to a few of the cities you've mentioned and have some insight as to some fun places to check out...
New Orleans - Obviously the French Quarter is where you will find some great restaurants and if you're into music I suggest checking out the legendary Tipitina's jazz club. Magazine street is good for shopping and there are some neat funky neighborhoods around there. The garden district is also a must see if you want to check out neat southern architecture.
Savannah -
Charleston - Sullivan's Island is a fun place to spend the day on the beach and there is a popular restaurant which is walkable from the beach called Poe's where a lot of locals like to hang out. Market street is a strip of open-air markets that is fun to walk through and there are great restaurants and shops around there.