Not quite sure where you'll be but I second the recommendation on day trip to Charleston--or day trip 2 hrs in the other direction to Asheville NC (probably a little cooler). Beaufort down by GA border is also a really cool old town (and close to Savannah).
If you like nature, the Congaree swamp just outside Columbia is a cool place to explore, though this time of year you'll want to marinate in DEET prior to heading out there. If you like to canoe/kayak there's some great paddling on the Edisto and Pee Dee, or up around Lake Jocassee. (DEET marinade also recommended for the Edisto, and I wouldn't take kayaks on the swampy stretch near Orangeburg as you'll be climbing over lots of blowdowns).
Have a good visit!