You can also feed the giraffes at Riverbanks Zoo.
3 art museums Gibbes, McKissick, & Columbia Museum of Art (unless I'm confused and Gibbes isn't in Columbia, can't remember). I've only been to the Columbia Museum of Art and if you aren't really into that, the price seems kinda steep.
A couple of places will rent kayaks/canoes or inner tubes and drop you off & pick you up on the Saluda River.
If you didn't bring a weapon and want to shoot, there's an indoor range where you can rent handguns on US 378 in West Columbia called Shooters Choice. Sometimes it gets crowded, best weekend time used to be Sat before noon. Haven't been there to shoot in a long time since I found the free outdoor range.
Famously Hot Music Festival. Weekend of Aug. 25. Friday is EDM (had to look that up...Electronic Dance Music), Saturday is "rock" day with 5 or 6 90's Alternative bands (Eve6, Soundgarden, Buckcherry forget the others), Sunday is "country" day. It's at Finlay Park in downtown Cola and I think the tickets are $20/day with no 3 day passes.
Always can stay on base an harass the recruits...oh wait, the Army gives their recruits weekends off don't they?
I think there's a MX course out off I-20 east of Cola headed towards Florence.
There used to be 2 places to rent boats on Lake Murray. One was pontoon only, the other had regular boats & jet skis but I'm not sure if they survived the recession. There were also 2 dinner cruise boats on the lake last summer. Most of these were out of marinas near Chapin on the NE side of the lake.
Horse stuff in Aiken, not sure if there is anything going on while you are here.
Might want to check if there are any concerts on base. There used to be a tour sponsored by the US Army that would hit Ft. Jackson each summer. Concert was at the outdoor stadium on base.
There are a couple of other concert venues in/around town. Colonial Life Arena, Township Auditorium, and the Newberry Opera House. Might be something to see there.
We have a minor league baseball team the Columbia Blowfish. Not sure if their season is over yet, but it is near the end.
Couple of theaters for plays if that is your thing. Town Theater, Trustus, and there is one affiliated with USC's drama department.
If you are into air shows, there might be something happening at Shaw AFB, McEntire ANG, or Owens Field. Sometimes they have vintage aircraft at Owens or the Thunderbirds/Blue Angels in the area.
Just tossing' out ideas, haven't actually checked any interwebs to see if any of these are going on.