Slaughter Creek Trail
a.k.a. Slaughter Gap Trail
The trail provides easy access to the Appalachian Trail. It crosses its namesake creek at about 2.2 miles, then turns uphill toward the gap. Although the hike is mostly uphill the whole way, it does not turn into an extremely steep ascent when it nears its junction with the AT (like most other access trails do).
For a longer hike you may wish to make a loop out of Slaughter Creek Trail, the Appalachian Trail, and Jarrard Gap Trail, which, all total, would come to about 6 miles.