Virginia has lots of public hunting lands. West of Fairfax is Thompson WMA, which is loaded with bear, deer, turkey, and squirrel. There are several other WMAs within an hour or so of Fairfax. The GWNF isn't much further.
Hunting pressure can be moderately high on weekends, deer opening day, and deer either sex days. Weekdays and black bear season tends to be light. If you go deep into the woods, the hunting traffic drops off to nothing.
Maybe a NoVA-PF day hike at Thompson is in order?
These are critter pics I took at Thompson with my game camera (except for the print, I took that with my phone, the cartridge is a 308win):
I have a lot of bear pics from that season. One of those two chewed up one of my cameras.
Chris