Since you're near, drop by Beaufort, and Hunting Island State Park.
Don't know what you are interested in, but Columbia consists of the University, State House, Fort Jackson, Riverbanks Zoo, and the State Museum. They are developing the river area more and more and has some nice restaurants and bars. The places to camp are limited there are a few private campgrounds but three state parks "In the area". Dreher Island on Lake Murray, Sesquicentennial State Park near Columbia, and our favorite, Lake Wateree State Park.
If you go to Augusta which I don't know much about other than that golf tournament, you might drive through Aiken SC which is a wonderful old town, famous for Polo, old money, walking gardens.