I'd go some where else. There are a lot of horror stories about people getting busted in National Parks. Hopefully this will be changing next month.
Blue Ridge Parkway: Things Recreational
Hunting - The Blue Ridge Parkway is managed as a preserve for wildlife. No hunting is allowed, and all weapons from slingshots to shotguns are carefully controlled. Spotlighting wildlife at night is also illegal. Loaded weapons are illegal inside the park boundaries. When traveling on park roads, all weapons must be unloaded and either rendered inoperable or inaccessible. Concealed weapons are illegal on park land even with a state permit.
USAF Retired, CATM, SC CWP, NH NR CWP, NRA Benefactor
To preserve liberty, it is essential that the whole body of people always possess arms, and be taught alike, especially when young, how to use them... -- Richard Henry Lee, 1787