Great Smoky Mountain NP on the NC-TN line. Mountains and trails all over the place, backcountry camping allowed with permit. The Appalachian Trail starting in GA, ending in Maine, runs the length of the mountain chain, accessible by road in many places. Or for one-day hikes, DuPont State Forest near Brevard, NC. Lots of trails and watefalls, CG's all around the area.
Jim, "Mo' coffee!"
On edit: I forgot to mention that there are several areas of Pisgah NF that are accessible from the Blue Ridge Parkway in NC... the Art Loeb trail that crosses the P'way near Devil's Courthouse & Black Balsam trailhead; trails around Mt Mitchell SP; trails around Grandfather Mtn. Stay safe, and have fun!
'06 Tiger CX 'C Minus' on a Silverado 2500HD 4x4, 8.1 & Allison (aka 'Loafer's Glory')