I've got to tell you this: I love Carolina North at UNC Chapel Hill. The last time I lived in Chapel Hill I rented an apartment right across the street from Carolina North so I would just run across the street and hop on the Pumpkin Trail for my regular run. The Pumpkin Trail is a local area favorite: there are UNC students, community running groups, local area high school cross country runners, neighboring folks out walking their dogs, trail runners, annual Pumpkin Run and Philosopher's Way participants, power walkers, mountain bikers, and all other variety of people.
The Carolina North Forest (usually just called "Carolina North" but also known as the Horace Williams Tract named for the philosophy professor who bequeathed the property to the university) is owned by UNC Chapel Hill and is easily accessible via MLK, Jr. Blvd (Hwy 86). The forest has a few twisty single-track trails that are more popular among trail runners and mountain bikers, but the Pumpkin Loop is a very popular wide dirt/gravel trail that's about 2.5 miles long. Access it from Municipal Drive off Hwy 86 (MLK, Jr. Blvd.) and start where the pavement meets the gravel or drive up the gravel a bit to the parking lot for the trail. The Pumpkin Loop itself is just 2.5 miles but if you run the gravel access from Municipal Drive and back that will put you just short of 3 miles. You also have the option of doing the loop multiple times or exploring the single track trails to tack on more mileage.
The Pumpkin Loop is a pleasant hike or run with just enough elevation change and twists and turns to make it interesting, but not so much that it isn't accessible to those newer to trail running and hiking. (This was my first ever trail run and still holds a special place in my heart).
I recommend the trail for spring or fall when the hardwoods look their best, but it's a great option year-round. Bring water, be mindful of signs posted at the gate, be respectful and don't get on the single-track trails if they're closed - usually right after heavy rains, and enjoy the peaceful greenwood tucked in the heart of Chapel Hill.