In Charleston, I would recommend one of the carriage rides. We started our day at the central tourism point - it's an old train station. That's where you can buy all of your tour tickets. There's a transportation system that you can buy a one-day pass for - which will get you everywhere. You can also buy your carriage tour tickets, there. Someone has recommended the restaurant at which we ate lunch on the board before, but, for the life of me, I can't remember what it's called. Something about ribs?!? Oh well - there's plenty of places to eat! We also enjoyed driving into the Citadel. You may get lucky and be able to catch some of them doing their drills out in the central courtyard - it was fun to watch. Be sure to drive down near the Coast Guard station, then up the stip along the water - there's some BEAUTIFUL houses to see there!
In Savannah, I would shoot for one of the seafood restaurants down on the water - they're all good, and are in a good location. We did the carriage tour here, also, and enjoyed it.
Wish I could offer you more specifics - it's been several years since we went. Stop by the front desk and get recommendations from them! Also be sure to get their driving directions to Savannah - there's a shortcut that saves you some time from driving all the way back out to I-95.
Also - if you have time - take a trip over to Beaufort. It's much closer than Charleston, and much smaller, but a very pretty town. There's a lighthouse a few miles out from there on a point in a state park - it's REALLY pretty. And, of course, there's Parris (sp?) Island. The day we went, we drove in and went right to the information center, then boarded a bus for a free tour of the facility. But, with the current situation, you probably won't be able to get on base. Let's all pray things are different when you go in May!
Finally - don't forget your Skin So Soft, or similar remedy. The no-see-ums are going to be tough that time of year! Have a great trip - we haven't been up there since '99 - I'm ready to go again!