If you go to Natural Bridge or Crabtree Falls, be prepared to see lots of other people around. Like DBP said, Shenandoah and the Blue Ridge Parkway have lots to offer.
To expand a little on Mike's idea of places around Richmond, it's overdone by every photography student at VCU, but Hollywood Cemetary is still a pretty neat place to go.
There are dozens of vineyards and wineries all over Virginia, Tamworth just west of Richmond off Route 45 has some old abandoned buildings damaged by Hurricane Camille, Barboursville Vineyards has some ruins on the grounds. Douthat State Park is a nice park, Warm Springs is a pretty area, Mt. Rogers/Grayson Highlands area, just so many places.
Just get in the car and drive west, you'll find something. Choose either Rt. 360 or Rt. 60 or Rt. 33 or Rt. 250 or Rt. 6 and just drive.