Parking in Chicago is super expensive so if you can, I would take the Rock Island Metra train which you can pick up in Joliet (about 1/2 hr. from Wilmington). A weekend family fare pass will cost $7 and kids under 11 ride free with a fare-paying adult. So, it should be $21 for your family round trip. That's less than parking the car in the city! I'm not sure if there is a parking fee on the weekend at the Joliet station (if so, it's probably just a dollar or two). Go to Metrarail.com to get more information on cost, schedules, etc. I don't think there is a ticket agent on duty on the weekends so you can buy the tickets on the train. Beware...if there is a ticket agent on duty, you will pay a surcharge on the train. The ride will take about 1.5 hours. The train station in Chicago is LaSalle Street Station located in the Loop at LaSalle and Van Buren.
Once there you can walk to the Willis (formerly Sears) tower and walk on the new see-through ledges. Tickets are a bit pricey ($15 for adults, $10 for kids). You can also walk down Van Buren to the Harold Washington Public Library. It's really a neat place (and free). The Wintergarden on the top floor (9th I think) is really beautiful and offers some good views. Then you can continue on the Art Institute of Chicago. It's $18 for adults and children 14 and under are free. After that you can stroll down Michigan Avenue. Make sure to go to Millennium park where Cloudgate or as we affectionately call it "the Bean" is located.
Your best bet for to get a real "feel" for Chicago is to take a long walk down Michigan Avenue (or take a cab). You can go to the John Hancock Observatory. You'll also get fantastic views (prices are the same as Willis for a basic pass) and there's so much to see nearby. Close by at Water Tower Place is a HUGE American Girl doll store. Of course, everything there is pricey but it's so fun to walk around. There are many stores on Michigan Avenue and restaurants. The John Hancock Building has a Cheesecake Factory on the ground floor but be prepared for a wait. The portions are HUGE so we usually share some appetizers. Also close by is the a new, huge Hershey's retail store and a Grand Luxe Cafe (owned by Cheesecake Factory). Your nose will lead you there. For cheaper casual eats, I like Potbelly Sandwich Works, Billy Goat Tavern (cheeseboiger, cheeseboiger) and Cafe Salsa all of which are on Michigan Ave.
http://www.urbanspoon.com/npr/2/130/1/Chicago/Magnificent-Mile/Cheap-Eats.html
There's also Navy Pier located at 600 E. Grand (you'd probably want to cab it from LaSalle Street Station). If you drive, there's parking right there. Check out Navy Pier's website for things to do there...many of which are free. You can always walk from Navy Pier to Michigan Avenue to go to the John Hancock building, Water Tower Place, etc.
Hope you have a great trip and good weather!
Kate