I live in Radford. Welcome to the NRV (or welcome to shooting if you lived here already).
The closest range to Blacksburg is the NF range off of Rt 460. Take 460 out of B'Burg toward Bluefied. take the first right after the first National Forest sign. Then take the first left onto the road going up to the range. If you get to Pearisburg, you missed the turn.
The range is unsupervised and allows you to shoot anything you want. Just clean up after yourself. There probably won't be too many people using it this time of year, but it can get very crowded (and potentially dangerous)around the beginning of firearms deer season.
Bring a spotting scope and something to hang your targets from. When I used to go to this range I usually used cardboard boxes as target stands. The spotting scope will let you observe your groups while others are firing. If the place gets crowded, it can be a long time between cease-fires.
There is also an indoor range in Roanoke, PSS Range & Training. It is a fairly nice, handgun-only, indoor range. Look them up in the phonebook and call for directions and hours.
If you are interested in competition, Roanoke Rifle and Revolver Club will start their matches in March. The competitions are open to the public and the club also has a skeet, trap, 5-stand, and sporting clays ranges that are open tot he public on weekends. The club has a web-site which lists directions and match schedules.
www.roanokerifle.com