Definitely check with the office. I am sure you may be able to register on line and pick up your tag when you arrive and drop your payment in the honor box.
The parking fee is per day. We also worry when a car is left at the park overnight (someone may be lost hiking) so check with the park office.
Not sure about parking in there state park overnight but you can park off of Liberty Hill Ln or Blue Ridge Mountain Rd and hike the Appalachian trail
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