Both large zoos are excellent. Lincoln Park Zoo is near the downtown. Brookfield Zoo is in suburban Maywood, John Prine's hometown. Brookfield is really large, wonderful, but may be too much for young kids. Lincoln Park is more kid scale. Field Museum is excellent, for dinosaurs, mummies, large taxidermy (elephants, etc.).
A good downtown kid place is Millennial Park, near the Chicago Art Institute and the lakefront. The Park is kid friendly, has a sort of fountain wading pool, a huge chrome kidney bean that reflects the fabulous skyline but doubles as a funhouse mirror. These are in the general neighborhood of Iwan Ries on Wabash, maybe a short cab ride with kids.
Not for young kids, but worth seeing if you get a chance, is the Chicago Art Institute with its vast collections. To keep it from being exhausting, maybe focus on French Impressionism and Modern. If that's your kind of thing.
You can spend a lot on food at upscale restaurants in Chicago. But if you are out in neighborhood shopping areas, you can find great international food in specific neighborhoods where immigrants settled generations ago. Ask around. Polish, German, Hungarian, Lithuanian ... some you just don't find elsewhere, and at neighborly prices.
There are good boat tours on the Chicago River that would entertain kids and give a spectacular view of the city's famous architecture without having to walk miles.
Chicago is a great tourist city, and a little less overbearing than NYC, though I love the Apple. Preview all my suggestions online and/or with a tourism book, since it's been a long time since I've roved the city.