You may legally ride your ATV in Virginia's two national forests, the George Washington National Forest and the Jefferson National Forest. You must purchase a permit from the forest service in order to do so, however. ATV use is prohibited from late January through late March due to damage that could ensue during freezing and thawing. ATVs may be operated on private property, but operators must have written permission from the propertyowner.
Check out these Alexandria, VA ATV/OHV resources: