There is a barn called Irish Oaks in Irmo that now where the USC club team rides at. I think Sinead Halpin use to be there, don't quote me though. I am located in Columbia, are you looking for something specific?
Friend of mine, who is getting back into horses after an extended haiatus, is thinking she may have to go the hunter/jumper route since there are no eventing specific facilities in the area. I told her that I thought there was an eventing barn in Irmo (I believe it was Sinead Halpin that I was thinking of at the time, not realizing that she's no longer in the area), and she was excited about the possibility of sticking with eventing, rather than the world of line, diagonal, diagonal, line.
Kathy Faulk trains up there. She used to be at Farewell Farm in Blythewood, but Farewell is no longer a functioning facility (used to run recognized there) now its just a few private horses but there is still a nice xc course kept there.
I am not sure off the top of my head where Kathy teaches now but it is right down the road from Farewell. Many of the eventers that used to ride at Farewell still ride there with her. (Mollie was a working student there some years ago). I believe the new farm is a jumper place, but all of those eventers board there and lesson with Kathy. Look her up.
I love Kathy! She works out of Glenwood, but also may drive and teach at your facility. She always comes to my barn for my lessons. If you would like to contact her or find out more about her, pm me. But like everyone else is saying, there isn't much eventing in the Columbia area as far as eventing barns go. I have boarded at a dressage barn and brought in Kathy and trailered out to Glenwood and Aiken for lessons. Lellie Ward at Paradise Farm in Aiken is lovely if you want to board in Columbia and trailer to Aiken.