Wow ... I finally get recognized as a Gamecock. Hope they don't pull the el-foldo routine when they tip-off tonight against Memphis in the NCAA!
I've been back to my alma mater quite a few times and many of the layouts already mentioned are worth a look.
Let me also mention from a public perspective you have Richland County's LinRick Golf Course just north of town. I used to play it plenty of times when at school and the layout isn't that bad. If memory serves -- the long par-5 16th was really a neat hole as it double-doglegged throgh the pines.
Couple of others worth noting -- try Persimmon Hill in Johnston-Saluda -- about 60-75 minutes due west of Columbia off Hyw 378 -- again if memory serves. The course is loosely patterned after ANGC -- two of the par-5's play over ponds -- I believe the 8th and 11th holes and the fees were always quite reasonable -- save for Masters time when tee times become a bit more difficult to secure.
I always enjoyed Columbia CC -- as previously mentioned an Ellis Maples design. One of my professors -- a good friend -- used to say that he thought Columbia CC was the best in the immediate area. I won't go that far but the layout is quite strong -- especially if you play from the tips.
If you have access you can also try Fort Jackson's golf course. There were a few changes made to the course -- I believe Maples might have done that too.
Clearly, if you can gain access to Musgrove Mill in Clinton you will play one of the finest clubs in South Carolina that is VASTLY UNDERRATED from a national perspective IMHO. Turboe previously posted pictures and analysis on the course.
Enjoy Columbia -- if you're looking for some night life (a demanding thing for such a small town) I would recommend heading to Five Points which is no more than a mile from the center of the Univrsity. Plenty of beer joints and some decent grub as well. Ah -- those college days never leave you.