A cornerstone of local culture is the Overture Center for the Arts (201 State St., 608/258-4141, www.overturecenter.com [1]), home to myriad performing venues.
Grab a picnic basket and head for the Capitol Square on Wednesday evenings for free concerts put on by the Wisconsin Chamber Orchestra. Though the weather is incessantly bad for these concerts, they are wildly popular. The Memorial Union (800 Langdon St., 608/262-1331, www.union.wisc.edu [2]) at the UW is the most popular place to be Thursday–Saturday for its free concerts.
For family-themed freebies, always check the local Isthmus.
Links:
[1] http://www.overturecenter.com
[2] http://www.union.wisc.edu