Since you're in Fort Lee, the closest public hunting land would be Chickahominy WMA. Go over the Harrison Bridge at Jordon Point and pick up Route 5 east. Take that a little ways past Charles City and then follow the signs into Chickahominy WMA.
http://www.dgif.virginia.gov/wmas/detail.asp?pid=1

As with most public WMA's in Virginia, it's best to try to go during the week. Saturdays can be extremely crowded and utterly ridiculous, not to mention almost downright scary! During firearms season, there will be so much blaze orange, the place will look like a flippin' pumpkin patch!!

From one New Yorker to another (I grew up in Poughkeepsie, NY and still have lots of family and friends still up in NY), let me give you a quick "heads up" about Virginia.

* There is no hunting on Sunday.
* East of the Blue Ridge Mts during firearms season, people deer hunt with dogs.
* West of the Blue Ridge Mts, it's wide open country. But, it's a loooooong a.$.$ drive - especially from Fort Lee, and they don't run deer dogs.
* Last but not least, do what I did this past season: Live here, work here, but choose to not deer hunt here. I went back home to upstate NY and hunted on my sister & bro-in-law's horse farm, and even got a nice buck - ON A SUNDAY!

Where are you from in New York?