The winning city, without any doubt, is Washington, D.C.
Also beating San Francisco:
Houston, TX
Huntsville, AL
Pearlington, MS
Kennedy Space Center, FL
Dayton, OH
Seattle, WA
San Diego, CA
Chantilly, VA
Ashland, NE
Unless you actually go to the same museum again and again, your own city doesn't matter. To see different things, you have to travel to different cities. The best city is thus one with lots of cheap direct flights to the cities with museums. That would likely be Denver, Dallas, Chicago, or Atlanta.