Most of the camping around the track is not affiliated with Richmond International Raceway. With that said the camping you will find around (walking distance) the track is dry camping. Most is first come first serve. A popular spot is the Azalea Flea Market.
One campground we have been to years ago is Kings Dominion
in Doswell, VA. This campground is around a 20 min drive from the track and offers hookups and shuttle service to and from the track for the cup race.
If you are looking for more information on camping at any of the NASCAR track visit Nascar Camping
, then click on NASCAR Forum on the right side of the page.
We have been going to Richmond, Bristol, Dover since 2000. Hope this helps.