State Street connects UW and the Capitol. It's a pedestrian mall with only busses running, no cars! There many restaurants, coffee shops, bars, and opportunities to shop. It's about a mile from UW to the Capitol. The Lowell Center is just one block from State Street.
Our Favorite Shops on State Street:
More info at Shop Downtown Madison.
This video is from 2014 but give some nice views of State Street Shopping.