I went to MS&I in chicago a few years ago on a free day and it was a mad house. I would suggest paying admission it is a lot less bussy and worth the admission to avoid the crowds.
Hi Gang, Ellory from Chicago here. It's true that Chicago is a great place to visit. Here's another tip. Check out the Field Museum and the Museum of Science and Industry Calendars before you go. They too have free days! This does not include special events or special exibits. But hey...free is free! And there's alot to see without the special stuff!
In Los Angeles, there's this great place in Manhattan Beach called Sand Dune Park, with a playground and a huge sand dune kids love to climb down. It's a real challenge for them! You climb up on wood stairs to the left side of the dune, through a jungle-like kind of setting, and then it's a sandy, steep leap to the bottom. Last time we went it was uncrowded, easy, and so much fun! Totally free, of course.