Every Saturday from 8 am - 12 pm, Durham Central Park hosts a farmer's market where over 50 vendors sell locally-procured food, crafts, and art (nothing at the market can come from more than 70 miles away). Grab a coffee while while you browse for something to remember Durham by. The Durham Food Hall is right across the street too.
UNC is just a short drive from Durham, and its campus is a great place to spend a few hours on a sunny day. Take a sip from the Old Well, see the oldest state university building in the nation, tour the arboretum, and end on with a Blue Cup at He's Not Here on Franklin Street.