I lived in Chicago for 3 years, but it was 10 yrs ago so my knowledge is a bit out of date.
But just to add to what others have said, if you can get a babysitter for an evening, you should check out one of the blues or jazz bars.
There are a lot of great public spaces with very cool sculptures which your kids might enjoy.
Chicago Art Institute is world class, but probably not great with kids in tow.
And, depending on time of year you are there and weather, you can go to the beach. Oak St is the cool one, there will be others for families.
Go out for a proper brunch at the weekend.
Wicker park used to be the funky arty area but maybe that has gentrified now...
And don't even consider driving -- no so much the traffic, but parking is impossible in the centre of town.
Another tip is that restaurants serve huge portions (you will see a lot of obese people) and it is quite acceptable to share a single order between two. It's almost expected that you will ask for a doggy bag to take away what you can't eat there.
Also there are always festivals going on particularly during the summer -- there is a weekly free newspaper called The Reader which is available everywhere which tells you what's going on.
Enjoy!