Here are links to the websites of museums with space-related exhibits.

Alabama
U.S. Space & Rocket Center

California
California Science Center
San Diego Air & Space Museum
U.S.S. Hornet Museum

Colorado
Wings Over the Rockies Air and Space Museum

Florida
Air Force Space & Missile Museum
Kennedy Space Center
Naval Aviation Museum
Space Walk of Fame
South Florida Science Museum

Illinois
Adler Planetrium
Museum of Science & Industry

Indiana
Virgil I. Grissom Memorial Museum [ no website ]
PHM Planetarium & Air/Space Museum

Kansas
The Cosmosphere

Michigan
Michigan Military and Space Museum
Michigan Space Science Center

Missouri
Greater St. Louis Air & Space Museum

Nebraska
Strategic Air and Space Museum

New Hampshire
McAuliffe-Shepard Discovery Center

New Mexico
New Mexico Museum of Space History

New York
Cradle of Aviation Museum
Intrepid Museum
New York Hall of Science

Ohio
International Women’s Air & Space Museum
Neil Armstrong Air & Space Museum

Oklahoma
Stafford Air & Space Museum
Omniplex Science Museum
Tulsa Air & Space Museum

Pennsylvania
The Franklin Institute

Texas
Frontiers of Flight Museum
Houston Space Center

Virginia
Virginia Air & Space

Washington
Museum of Flight

Washington, D.C.
The National Air & Space Museum

Wisconsin
Deke Slayton Memorial Space & Bike Museum
Mitchell Gallery of Flight
Tony Bartlett’s Exploratory

England
Science Museum, London, UK