I live in the Cincinnati, Ohio area and for aircraft fans nothing beats the Dayton Air Force Museum about 45 minutes north of the city. On site are aircraft from the beginning of flight up to the bombers, fighters and drone aircraft of today and most are touchable.
When traveling abroad I have visited the Musee D’orsay in Paris a number of times for their remarkable sculptures and paintings. I also agree with Josh that the Musee des Arts et Metiers is a must for engineers and tech geeks like myself.
I intend to investigate some of the other Paris museums mentioned by responders and appreciate their suggestions.