There are precious few hiking opportunities in northern Durham and Orange Counties counties, which is unfortunate. The Piedmont hills here rise a little higher, the air temperature a wisp cooler (sometimes to the point where a winter rain throws cold water on a hike in Raleigh, it blankets northern Durham/Orange with an inviting layer of snow). Fortunately, there is at least one option: Little River Regional Park.
This relatively new (2004) 391-acre park includes 7 miles of hiking trail and 7 miles of mountain bike trail. While the annual Little River Trail Run includes the singletrack mountain bike trail in its 10-mile option (which you can find here) the route we suggest sticks to the hiking-only trail and runs about 5. (We eschew the mtb trail because there's enough hiking trail here that we can; some runners aren't comfortable sharing the trail with fleet-of-tread mountain bikers.) From the parking area head down the gravel road near the rest rooms for a quarter mile to the main trail junction. Here, pick up the 1.8-mile South River Loop Trail, which will give you a taste of the Little River and the hardwood forest that dominates the preserve. The loop brings you back to the trail junction; this time, take the Ridge Trail, a 1.5-mile out-and-back. This trail climbs a mellow ridge to its apex. Here, pick up the 1.2-mile North River Loop, which takes you down to the stream, then back up to the top. The mellow descent back down the Ridge Trail and the short, quarter-mile climb back to your car is a nice way to end your run. More info: Triangle Land Conservancy here; Orange County Department of Environment, Agriculture, Parks & Recreation (site manager) here and at 919.245.2660 (park office); Eno River Association here. Maps: Triangle Land Conservancy here, also available at park office. Getting there from downtown Chapel Hill here.