Sorry I didn't see this sooner. There's a good bit of riding, plus a brand new 250m velodrome in Rock Hill. You can race basically any weekend you want to in some fashion. Check out 36th Street Racing, that's the club I'm with, they have a few rides a week that are good for getting to know people, racers from various teams are there. Very active team with lots of racing and group riding and hanging out.
Orr Rd crit on Tuesday nights is also a great place to find out who is racing, which teams you like and don't like, etc. It's an unofficial office park crit, P/1/2/3/4/5/6, not official, but that doesn't mean it isn't fast. You can find out more on weeklyrides.com as someone mentioned, it's an amazing resource (and a sponsor of my team, for disclosure).
Which part of town are you in? I'm in University but 36th Street is based in NoDa. Orr Rd is between my house and NoDa.
I'm usually out on the Thursday and Sunday 36th Street rides, as well as Tuesday when I feel like getting my teeth kicked in. Presbyterian Sports Medicine (also Uptown Cycles is a title sponsor) kit or often NC State kit, on a Ridley Noah. I'm hard to miss, I'm the guy off the back on the nice bike.