Well, I was going to suggest the beach but it looks like you are in northwestern VA, so that idea isn't going to do you much good!
Unfortunately it doesn't look like VA state parks (like most state parks) are not particularly detecting friendly. Here is the regulation I found listed on the FMDAC website:
"§1.13 Metal Detectors
No person shall use a metal detector or similar device within a park without the express written permission of the Park Authority."
What that appears to mean is you have to ask permission first. What that means in the real world is that detecting is not allowed. I guess it wouldn't hurt to ask, but don't get your hopes up. Probably better to stick to city and county parks rather than risk state.
Looking at a map I see you are close to a National Forest. Those are ok to detect for the most part, just keep clear of any areas that could be considered to have archaelogical artifacts. When I say National Forests I mean National Forests, NOT National Parks, National Wildlife Areas, National Monuments, etc. as those are strictly off limits.