You can get a backcountry permit from the Ranger station and go anywhere that is not off limits like, the summit of a mountain or a popular waterfall. Permits are free
There are lots of options for backcountry if the campground is full. Pocossin Mission, Booten Gap, and Rapidan fire road are all near Big Meadows and intersect with the Appalachian Trail. Make sure you register at the entrance station!
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