If you don't want to do the dirt, you can ride along Skyline Drive for over 100 miles. However, if you do want real MTB, be sure to take a topo map to Shenandoah. The best way to do is to go explore or to ask a park ranger for trails.
How to get there:
From Richmond: Take Rt 64 west until you reach the Waynesboro exit. From there, get on the Skyline Drive and head into the park. Talk to a ranger if you want to get some more trail info.