To gad is to wander without much purpose, aside from having fun. You might gad around town on a Saturday afternoon with your friends, looking for something entertaining to do.
If someone's roving from place to place seeking amusement, you can say they gad about. Your brother might gad about the neighborhood all day while you're at home diligently studying for a math test. As a noun, a gad is a tool with a point on it, like a chisel, and in the western U.S. it's also a word meaning "spur," the spike on a cowboy's boot used to encourage a horse to get going. This verb forms the noun gadabout, a person who restlessly seeks amusement.