Located in the historic Dearborn Station, the Jazz Showcase is a particularly good place to introduce children to Jazz. The venue is able to attract top-notch talent on a regular basis. During the club's 4pm Sunday matinees, all ages are admitted, and kids under 12 are free. For adults admission covers all of your costs, and you are not expected to buy drinks once inside (though a full bar is available). Reservations are recommended for "big name" acts.
Not every child will be able to sit through an entire performance, but most are more interested in live music than we parents realize, and this can be a wonderful way to connect with old Chicago during your trip.