There are options for parking at the great majority of places where the AT crosses a road. The real concern is whether a vehicle will be vandalized at the parking area. These are rare, but a frequently vandalized area is where the AT crosses 19E between Roan Mountain, Tennessee and Elk Park, NC.

If you could offer an idea for a region where you are interested in hiking, it would be much easier to give you specific parking options. You might also want to check the Appalachian Pages or ALDHA Companion for more specifics.
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http://www.trailjournals.com/BearpawAT99/