I agree with the above comments the James, little falls on the Potomac, and Shenandoah/Potomac in harpers ferry are all pretty good class III runs but also recommend the Rappahannock in Fredericksburg and the lower yough which is about 3 hours from Northern VA but is a great III+ river that runs year round. Also there are 3 good forums you should check out if you are looking for people to boat with:
Paddle Prattle Paddle Prattle
is the main forum in the DC area
Coastal Canoeists www.coastals.org
main forum for Richmond/central VA area, really nice club
Boatertalk BoaterTalk: BoaterTalk
the mountain buzz equivalent of the east coast
I live in Northern VA so if you have any other questions just let me know!