The Skyline Drive in Shenandoah NP is open, and it doesn't cost anything (the only officials I met today, were mobile Rangers keeping an eye out for stranded or speeding drivers).
There are dozens of hikes available. Just pick the trailhead with the least cars (social distancing) and you are in business.
Since there are no leaves out yet up there, you can enjoy also great views.
Sent from my Samsung Galaxy smartphone.