http://www.naturalbridgeva.com
This is a paid attraction for $12 (kids under 5 are free), and there are other discounts for the other attractions (caverns, wax museum). You can take the free bus ride or walk down several scenic steps to get to the Natural Bridge.
The rock formation is 215 feet tall and 90 feet wide. As you continue on the trail, you'll pass through the small Monacan Indian Village, where they have reenactments and you can ask them questions. Farther along the trail you'll follow Cedar Creek and pass Saltpeter Cave, where they mined for nitrates to make gunpowder during the Civil War. There is also The Lost River, visible through a low arch in the side of the mountain, its sparkling waters flowing from an unseen cavern above to one below the creek. And at the end of the hike is Lace Falls, with small cascades along the 50-foot drop.