Statehouse downtown, real neat history. +1 on a baseball game if anyone is playing. You could also check out Lake Murray Dam, if the weather is nice. Lots of good places to eat in the vista downtown.

Forgot to mention, in addition the the SC State Museum, there's the SC Confederate Relic Room & Military Museum on the same property.

https://www.crr.sc.gov/visit

Palmetto Pig is a good BBQ place downtown. Little Pigs out on Alpine Rd. is even better.

Other good dinner places downtown are Motor Supply Co, Blue Marlin, Terra in West Columbia, or Al's Upstairs.

If you need a lift to Palmetto State Armory just let me know!