Savannah is nice ... Signature and Savannah Aviation are the two FBOs. You will need a crew car or rental car to get downtown, as it is a 15 minute drive or so from the airport. Neat historical town to be sure. Only time I was there was a short layover and all I ate was room service, so I defer to the suggestions of my fellow JC-ers.
Charleston is fantastic ... I always use Mercury at CHS ... CHS is a joint civilian-military facility with a lot of miltary traffic, fun to watch. Lowcountry cooking is excellent ... take some of the other suggestions from folks whenever you go there.
If you go to Memphis, don't waste your time going to General Spain ... GO TO MEM!!! It is not as close to downtown, but you can see the FedEx push if you're around at night (and it is worth it) and you can visit the BEST FBO IN THE COUNTRY, hands down, Wilson Air Center. Get a crew car and go to Corky's on Poplar Avenue for some excellent barbecue. If you're overnighting, Wilson has a rate at the Hampton Inn & Suites at Peabody Place downtown. Stay there, walk over to the Peabody to see the "duck march", eat dinner at the Rendezvous (another good barbecue joint) downtown, and walk up and down Beale Street to see all the clubs and sights. Of course, there's also the Mud Island Museum and the Memphis Belle.
Enjoy ... all three are premium destinations on my list ... good sights, good history, good food! And all a reasonable flight from about anywhere in the Southeast.
Russ