Greenbrier State Park in Maryland is pretty close and open. Right off of I70 past Frederick. 1.25 hours away (with no traffic). The Appalachian Trail passes through the park. There's a trail from the campground to to the AT. There's a lake but it's kinda silted up.
Check out http://www.dnr.state.md.us/publiclands/western/greenbrier.asp
(I don't think this is considered to be a commercial link)
Bryan