State Street

The pedestrian-only street that runs between the Capitol and the UW Madison campus. The Capitol building itself is also pretty cool—you can just walk into it and wander around most of the time during the day, but they also have free tours if that sounds of interest. The square at the other end, at the UW campus, is across Langdon Street from Memorial Union (where the Union Terrace is that someone else mentioned here) and often has lots of good food carts out during lunchtime (although off the top of my head I'm not sure if that changes at all during the summer months).