Located in Ashland, Nebraska, the emphasis here is on military aircraft. However, there are some interesting space-related artifacts. They have a flown Block 1 Apollo command module which was used in a sub-orbital test. Plus, a few early satellites used to monitor Soviet nuclear bomb tests.
Maybe not worth a long drive to Nebraska, but worth a look if you are in the neighborhood.
The museum is located at 28210 West Park Highway, Ashland, NE 68003. The telephone number is 1-402-944-3100

