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Air Force Missile & Space Museum
Cape Canaveral

Located at the Headquarters, Eastern Test Range, Patrick Air Force Base, Florida, when I visited there in April 1965, it has since moved.

Fantasy of Flight
Polk City

Sadly, Fantasy of Flight closed in early 2014. A greatly scaled-down museum now is open only certain days. See their Web site at https://www.fantasyofflight.com/collection before visiting for days and hours open.
Visited 10 March 2013.

Merritt Island Veterans Park & Museum

National Museum of Naval Aviation

Visited 20 May 2015.

St. Augustine Museums