Buffalo Bill's Grave and Museum (Pahaska Teepee) on Lookout Mountain in Golden, CO. Just outside of Denver, this is a family, kid-friendly tourist destination. The views are spectacular and the museum is well done.
The Museum of Fine Art in St. Petersburg, Florida, is small but impressive. I've visited it more or less regularly for years, and they present quality exhibitions in a professional environment. A 2006 expansion allows the museum to offer a cafe and respectable gift shop, in addition to their permanent collection and revolving exhibits. It's a fine way to spend an afternoon, especially if you include the nearby Dali Museum in your itinerary.
Right on the water in St. Petersburg Florida is a modern and unusual building. The surreal yet sumptuous architecture of the Dali Museum is worth the experience, no matter what's on display. But you'll want to stay for the permanent collection plus whatever they have in the temporary exhibit halls, too.