Sarah P. Duke Gardens
Go for a walk in the Sarah P. Duke Gardens (http://www.hr.duke.edu/du...).
Eno River State Park
Go hiking or have a picnic at Eno River State Park (http://www.enoriver.org/) or West Point on the Eno. West Point has an old-fashioned corn mill that still sells fresh cornmeal.
American Tobacco Trail
Bike or roller-blade on the American Tobacco Trail. It's a paved-over railway line that extends from downtown Durham, near the ball park all the way to Raleigh. One section is not complete yet, so you may be stuck on Highway 54 unable to cross I-40 unless you bike on the roads. It is 7 miles from downtown Durham to the end of the trail at I-40 and Hway 54 junction.
Full Frame Documentary Film Festival
Attend one of the renowned annual festivals. Each April is the Full Frame Documentary Film Festival (http://www.fullframefest.org), the country's largest such festival, and each summer is the country's largest contemporary dance festival, American Dance Festival (http://www.americandancef...).
Ninth Street
Check out Ninth Street, a pedestrian friendly street with a variety of eating, shopping, and entertainment options. (http://www.ninthst.com/).
Hillandale Golf
Play on many different Golf courses from Hillandale Golf (http://www.hillandalegolf.com) to Willowhaven to the Duke University Golf Club among many more.
The Starlight Drive-In
Take in a film at The Starlight Drive-In (http://www.starlitedurham.com/); on a clear night, it is spectacular. Update: Since March 2007, this facility has closed down indefinitely following the death of its owner and is unlikely to open again.