St. Louis:

• Forest Park Museums
  • St. Louis Art Museum
  • St. Louis Zoo
  • St. Louis Science Center
  • Missouri History Museum

• Contemporary Art Museum
• Sheldon Concert Hall and Galleries
• Mildred L. Kemper Museum
• St. Louis University Museum of Art
• Museum of Contemporary Religious Art
• Pulitizer Arts Foundation
• Gateway Arch National Park – technically not an art museum, but has artistic elements and history worth visiting!

Springfield

• Springfield Art Museum

Columbia:

• Museum of Art and Archaeology

Fayette:

• Ashby-Hodge Gallery of American Art at Central Methodist University

Kansas City:

• Nelson-Atkins
• Kemper Museum of Contemporary Art
• Belger Arts Center
• Thomas Hart Benton House

St. Joseph

• Albrecht-Kemper Museum

Weston:

• The National Silk Art Museum

Poplar Bluff

• Margaret Harwell Art Museum

West Plains:

• Harlin Museum

Other points of interest:

• Hannibal – the town has several museums and living history exhibits. It is the hometown of Samuel Clemens aka Mark Twain