Depending on where you are in Richmond, there are two 1/4 strips near-by.
The first is Richmond Dragway, which is out in Sandston by the airport. The other strip is south of Richmond in Dinwiddie: Viginia Motorsports Park. VMP is by far the better track, but its a little more a drive to get there. Both venues run events every other (haven't been to one in a while) Friday night plus sometimes on Saturdays.

Welcome.
Not sure where you're from, but if you need a local shop for anything give my buddies Mark and/or Kevin a call @ Performance Autosport. (804) 784-8851.