The Tuttle (Okla.) Times has an article about aviation museums that are on or near Route 66 in OKlahoma.
There are probably more than you think. It includes Thomas P. Stafford Air & Space Museum in Weatherford, the Ninety-Nines Museum of Women Pilots in Oklahoma City, the Omniplex (which is building a manned space flight gallery) in OKC, and the Tulsa Air and Space Museum.