The Nature Trail, aka The Walnut Mountain Nature Trail, is the safest bet for a walk in the woods. It's the only trail section with benches where you can sit and rest and 2 picnic tables along the way. It's just over a mile from one end to the other and no one says you have to hike the full distance.
The trail head is on Wolf Laurel Road, just before you get to Big Bald Rd. It's advised that you hike early to avoid a common problem which is parking. An alternative to parking in the limited spaces on Wolf Laurel Rd is to drive up to Big Bald Rd, take a left and an immediate 2nd left onto Hanging Rock Rd. Drive the length of this road and as the road begins a noticible steeper incline, look to the right for space to park 2-3 vehicles. Park perpendicular to the road. Continue walking walking down the road a few hundered feet and look for signage on the left to the trail.