Benn Knob is listed as the highest peak in the South Mountains State Park. (I have my doubts, but haven't had a chance to check topographic maps.) The South Mountains are a fairly unusual sub-range of the Blue Ridge. They stand far to the east of the main bulk of the Appalachians, form the first ramparts in the area for high country before one encounters the Blue Ridge escarpment farther west.
The South Mountains.
(Addition: Benn Knob is definitely not the highest peak in the South Mountains. That honor goes to Buzzard Roost which is the highest peak in the range, and is now the highest peak in the park now that the size of the park has been doubled.)
While not very high, even by the standards of the Southern Appalachians, the South Mountains present extremely rugged terrain, spawn one of the cleanest watersheds in the entire USA, and are home to a fantastic array of tree species and rare plants. These peaks may not be so high, but the steep, rugged valleys and canyons that intersect the range make hiking from one ridge to the next a formidable prospect.
A nice map of the trails of South Mountains State Park can be found here.
From I-40 take NC 18 South. Drive for about ten miles (not the nine mentioned in park literature) and make a right onto SR 1913 (Sugarloaf Road). Take SR 1913 to Old NC 18 and turn left. Travel for four miles and make a right turn onto SR 1901 (Ward's Gap Road). Soon see the entrance road to the park SR 1904 (South Mountains Park Avenue).
This is one park that is not surrounded by development and is well out in a very rural area.
No special permits for hiking. The park is open year round. All of the common sense rules pertaining to plants, animals, fishes, flora, etc. apply.
When To Climb
Camping is allowed in the park. There is one semi-developed campground near the park entrance, and there is back country camping at designated sites (also semi-developed). Because of a series of roads in place in the park (built by the CCC), the backcountry campsites have some amenities not generally found in most such campsites: pit toilets, picnic tables, fire rings, and bear cables.
Fees are $9 per site, per night.
Check the weather for Morganton, NC. Subtract a few degrees for the highest peaks.