It might depend on what kinds of things you are interested in too...some ideas:

Henry Vilas Zoo is free and pretty decent (http://www.vilaszoo.org/)

The University of Wisconsin Arboretum has many nature trails (http://uwarboretum.org/)

Walking down State Street (a pedestrian, bus, and taxi only street with lots of shops and restaurants) is another good Madison idea

The University of Wisconsin Memorial Union Terrace is on Lake Mendota and often has live bands and always has reasonably priced food, ice cream, and beer (http://www.union.wisc.edu/venue-muterrace.htm)

If you want a pretty-authentic Wisconsin meal, The Old Fashioned is a favorite of many (http://www.theoldfashioned.com/)

If you don't have set plans of where to stay, the Best Western Inn on the Park is the only hotel on the Capitol Square and within walking distance to a lot.

The Farmers Market Saturday mornings on the Capitol Square is great during the summer - definitely try the spicy cheese bread (http://madisonfarmersmarket.com/)

Also, since the University of Wisconsin won't be in session, the campus-area should be less crowded.