The University of Wisconsin Geology Museum is one of those small, excellent university museums that gets overlooked in favour of bigger institutions. It is free, located in Weeks Hall on the UW campus, and contains a genuinely impressive collection of fossils, minerals, and geological specimens with particular depth in Wisconsin's own geological history.
The centrepiece is a mounted mastodon skeleton excavated from a Wisconsin bog, but the collection extends to meteorites, gemstones, a fine mineral display, and dioramas depicting Wisconsin's geological past — including the glaciers that carved the lakes the city now sits between. There are also fluorescent minerals displayed under ultraviolet light, which is always a crowd-pleaser.
This is a good option for a rainy afternoon or as part of a university campus walk. The museum is in Weeks Hall at 1215 West Dayton Street.