Grant Park in St Louis. Not a museum but a wonderful park full of animals,no admission, free trolly around the park and two free beers!

Lincoln Park Zoo in Chicago and the neighboring arboreatum. Not technically a museum but close enough.

My friend with a large family gave me this tip. Look into joining, even if you are there for a short time. For example, the St. Louis zoo is free, but they have a $10 ticket that covers admission to the children's zoo, insectatarium (sp?), and a train ride. You can buy a family membership that allows you over 20 admissions and train rides for $50, plus free parking. So, if you have more than five people with you, you would do better to join.

I can't even remember if some of my favorites were free or not. In addition to the big city museums, I like small town historical society museums - you never know what you'll see.

National Gallery of Art in DC no, wait, maybe the Hirschorn....it's pretty hard to pick just one...Library of Congress???

I truly appreciate all the free museums and sites available in my "home" DC area.