While not a climbing destination, Virginia still has a good bit of rock!
For roped climbing, Hidden Valley in Appalachia is a top sport climbing area and Breaks Interstate has good sport and trad routes. Great Falls and Old Rag also have a lot of climbs.
For bouldering, there are lots of crags around Virginia. Try out Grayson Highlands State Park, McAfee's Knob, Mill Creek, Blue Ridge Parkway the The Cascades.
There are lots of good guides for the area, including but not limited to: