If you are interested in a pleasant 3-mile jaunt on an asphalt surface, head on down to the Swift Creek and Symphony Lake Greenways. The beautifully wooded Swift Creek Greenway runs for 0.8 to 0.9 miles between Kildaire Farm Road and Regency Parkway. When you get to the end of Swift Creek Greenway at Regency Parkway, if you cross the road and go left, you will find yourself at Regency Park and Symphony Lake.
The mostly-open trail around Symphony Lake is a little over 1.2 miles long. The distance between the two trails is perhaps one-tenth of a mile so by running the length of Swift Creek Greenway, going around Symphony Lake, and back down Swift Creek Greenway, you will travel about 3 miles.
Convenient starting points are Regency Park and Ritter Park, both owned by the Town of Cary.
To get to Ritter Park, take Kildaire Farm Road from downtown Cary, past Tryon Road, to the light at Lochmere Drive West. Turn right at the light. The entrance to Ritter Park will be on your left. There is an entrance to Swift Creek Greenway at the back of the parking lot nearest the entrance.
The other starting point, Regency Park, is on Regency Parkway, on the right-hand side as you are going south, a little more than a half-mile from Tryon Road.