I live here, so I don't stay in many camp grounds. However, there are a few.
Depending on how close you want to be, Tanglewood Park is nice. It is located in Clemmons. It will put you about 15-20 minute from downtown, but does have lots of things to do before and after the race.
You could also go North a little to Mayberry.
I have never stayed at either, but have my first stay at Tanglewood booked for March. I go to tanglewood often, as they have decent single track mountain bike trails and lots of walking / jogging paths. I also ride to the park on my normal 50 mile route.
Are you racing or spectating? I'm a wannabe cyclist. I ride a Roubaix on the road and a Camber on the trail.
By the way... Lots of good road riding in this area, and some good single track within an hours drive.