We learned this the hard way — one surprise lake-effect afternoon and the whole outdoor plan is toast. Good news is Chicago's museums are genuinely world-class, and more importantly they're built for kids to touch things, not just stare politely.
Museum of Science and Industry
If you only have time for one, make it this. Kids can walk through a real captured WWII German U-boat, watch chicks actually hatching, and wander a full-size coal mine. It's huge, so go in with a plan or you'll lose the whole afternoon (and possibly a child) at the model railroad.
Field Museum + Shedd Aquarium
These two sit right next to each other on the Museum Campus, so you can pair them. The Field Museum has SUE, the most complete T. rex ever found, which never fails to get a proper 'whoa.' Next door the Shedd puts kids nose-to-glass with beluga whales and sea otters.
The practical bit
Buy tickets online unless you enjoy standing in line with a hangry six-year-old. If you're hitting a few of the big attractions, a Chicago CityPASS pays for itself fast. Strollers are fine everywhere, and yes, there's decent coffee for the adults.