You will find lots of opportunity on these trails: opportunity to get in some miles, opportunity to attack hills, opportunity to get lost. That is, unless, you invest the $8 for a detailed forest map (the online version referenced below is more of a general locator map; the link will tell you how to score the more detailed version) showing specific trails and specific access points.
The most popular divisions for recreation are the Durham Division, which begins near the Duke University in Durham, runs northwest to the Orange County line, then southwest, and the Korstian Division, which is in Orange County largely between Mt. Sinai Road to the north and Whitfield Road to the south. A good 4.5-mile route: park across from the firehouse on Whitfield Road near Sunrise Road (about midway between NC 86 and Erwin Road) and pick up the gated fire road/trail near the firehouse. The trail drops down to New Hope Creek then makes a steep climb for about 3/8 of a mile. About midway there’s a fork; go right. The trail loops back around, crossing New Hope Creek once again before coming back to Whitfield Road. Either take the road about a third of a mile back to your car or reverse the loop for a 9-mile run.
Invest $8 for the Duke Forest map and plot additional runs.
Getting there from downtown Chapel Hill
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Difficulty: moderate
Distance: 15 minutes from downtown Chapel Hill
Length: 4.5 miles (loop mentioned below; about 30 miles of run-worthy trail throughout the Duke Forest system)
Time to complete: 45 minutes to 1.5 hours
Address: 4012 Whitfield Road
City: Chapel Hill
State: N.C.
Zip: 27514
Latitude: 35.5859
Longitude: 79.0186