The Arboretum, Chapel Hill. Right in the middle of UNC's campus stepping in is like being whisked to the middle of a magical land. Great place to take pictures. Since I was a small child I have found this place calming.
Eno River Trail, mi - "Minutes from Durham and Chapel Hill, the Eno River State Park offers secluded wilderness trails with the serenity and sounds of the river. Take a break from civilization and march into the wild.