Take a look around the campus of UNC-Greensboro (http://www.uncg.edu). Good people watching and Weatherspoon Art Museum (http://weatherspoon.uncg.edu/) is fun on a rainy afternoon.
Visit the site of the historic Woolworth's Sit-In, a landmark in the 1960s civil rights movement. Elm Street south of Market, downtown.
Take a walk through Fisher Park, a 100-year old neighborhood surrounding a central park. Elm Street north of Fisher Avenue, downtown.
