Wildtoad told you a nice route that basically parrells the interstate. You will need to grab I26 then I77 to get through Columbia. The nice advantage is if you get tired of the slow driving and want to make some time, you can always jump back over on the interstate. You could also stop for a night at Lake Wateree SP which is one of the best SC state parks.
Here is an alternate route that takes you away from the interstate.
1) I26 to Hwy 27 (Exit 187) turn right (north). This is to avoid the town traffic.
2) At end, turn left on Hwy 176 (toward Holly Hill).
3) Catch hwy 601 north. Follow multiple turns until you get to Kershaw
4) In Kershaw, switch to 521 and follow north to Charlotte.
Just outside of Charlotte, you will go by Andrew Jackson State Park which has a nice small campground.
Couple side jaunts you can make:
1) If you like chocolate covered nuts, turn left on Hwy 33 in Cameron. About 1/2 mile on the left is
Golden Kernel Pecan Companya pecan place. Just check the hours to make sure they will be open. They have plenty of place to handle any size rig.
2) At Wateree on Hwy 601, if you have a couple hours, take a 12.5 mile detour over to
Congaree NP. Note there is a bridge out on Hwy 48 but it is suppose to re-open on April 16. If the bridge is still out, it would make it a 21 mile detour there. You can check
SC Road Conditions to see if it has been opened.
P.S.
If you like BBQ, make sure to stop in at Melvin's just up Folly Road before you leave town..