Cleveland Museum of Art
This museum is right along the lines of the St. Louis Art Museum and Kansas City's Nelson-Atkins Museum of Art. All are free, feature similar collections, and have interesting modern additions to their much-older original structures. They also all share a piece of Claude Monet's Agapanthus Triptych, surely his most the beautiful of his water lilies paintings. Cleveland's newish expansion features a huge, covered courtyard reminiscent of London's British Museum. A great way to spend a Saturday afternoon!