Saturday mornings and Wednesday afternoons you can enjoy the Durham Farmers' Market. There are experts at the market that can answer your questions and help you put together a wonderful meal including dessert options!
Durham is beautiful and has many outdoor activities available for your enjoyment. The American Tobacco Trail is a 22+ mile rails-to-trails project located in the Triangle Region of North Carolina. The route crosses through the City of Durham as well as Durham County. http://www.triangletrails.org/american-tobacco-trail
Eno River, Falls Lake, and Lake Michie are just a few opportunities to hike, boat, fish and swim in Durham.
It's not free but you can't think of Durham without thinking of teh Durham Bulls baseball team and park. Check their website for special deals especially hot dogs for $1! https://www.milb.com/durham