There is not much in the way of legal off roading this close the beltway. There is an offroad park near Winchester (google Big Dogs). There is also an OHV trail about a long hour away...

Taskers Gap Trail

There are also a few trails (I have never done them) near Harrisonburg.

Your best bet is to hook up with a local club. If you do not mind running with 'that other 4x4' , the local off camber club is pretty active and runs a lot of weekend trails.

It is almost criminal how much time my truck spends on the paved road. I wish I had more time to explore the Shenandoah Valley... but alas, I don't.