If visiting the upstate, the BMW tour in Greenville/Spartanburg is an awesome place to visit if you can get a spot. Greenville also has a coliseum that brings in some decent names, especially of the country variety, if that's what you're into.
Charleston is also a great place to go in the late spring or early fall. The city is full of culture and history such as Rainbow Row, the USS Yorktown, etc. Charleston also offers tons of great restaurants that marry soul food and seafood brilliantly. Just thinking of it makes me want some shrimp and grits.
Come with a hearty appetite because there are so many great places to eat that you will enjoy just trying all the different types of cuisine. From gullah, to southern, to seafood, to barbecue, to 5 star gourmet, you will not be dissapointed.