Check out the this site for what you can hunt, how much, and when.
http://www.dgif.virginia.gov/hunting/re ... llgame.asp
Here is a list of of Wildlife Management Areas in VA:
Gray and red squirrels may be harvested on all private lands and on the following wildlife management areas: Amelia, Big Survey, Briery Creek, Cavalier, Chickahominy, Dick Cross, Fairystone (including Fairystone State Park and Philpott Reservoir), Featherfin, Goshen, Hardware River, Havens, Hog Island (Carlisle Tract only), Horsepen, James River, Little North Mountain, Merrimac Farm, Pettigrew, Phelps, Powhatan (including the Goochland Tract), Rapidan, Thompson, Turkeycock Mountain, and White Oak Mountain.
Fox squirrels may be harvested on all private lands in counties with an open fox squirrel season during the regular squirrel season and on the following wildlife management areas: Big Survey, Goshen, Havens, Little North Mountain, Merrimac Farm, Phelps, Rapidan, and Thompson.