How far are you willing to drive? If you're willing to drive an hr or hr and a half you can hunt Rappahannock NWR. I've taken several nice bucks off the Wright Unit of Rappahannock. It's a quota hunt so you probably can't hunt it until next year but it is an option.
As others have noted you could also hunt Fort A.P. Hill. It's also an hr or so away. I've killed a lot of deer on that base. I've killed a bunch on Fort Pickett as well but Pickett would be farther to drive.