The University of Wyoming Art Museum is free to enter and houses a collection that would not embarrass a much larger institution. The American art holdings are the strongest, with good representation of the Hudson River School and twentieth-century Western painting, but the museum also runs serious temporary exhibitions that draw from national collections and travelling shows.
The building is on the northwest edge of campus, an easy walk from the UW campus centre. It is the best free cultural attraction in Laramie by a comfortable margin, and worth an hour whether or not you have any other reason to visit the university.