I just took my 9.5 year old DD to downtown Chicago a few months ago to get her first AG doll. I think there's plenty to do right there downtown without really venturing out of that area.
First of all, I would recommend getting a multi-use bus pass. When we got off the Amtrak, we were directed to a Walgreens across the street whcih sold the passes which were good for 2 days I think. It allows you to just hop on and off whenever you want.
If you have a smartphone, you can pull up on your phone where you're at, where you want to go and it will tell you exactly what bus to hop on. The buses are GREAT and we rode at least 6-8 times that day.....never waited any longer than 2 minutes!
Within walking distance of AG Place you've got the observatory (but kind of pricey to get in....just to look out from the top of a tall building!), Cheesecake Factory, a
Disney Store just down the street and GHIRADELLI!!!! Soooo yummy and a great treat for us. There aren't many of those shops around, so it was a special thing. Hershey's shop is just across the street, but honestly it didn't seem that special to us. A whole lot of stuff that you can buy at any store, but they did have a bakery which might have had some yummy stuff.
It would be relatively easy to get a bus to take you down to the Science Museum, Shedd, etc. However, those places will take a huge chunk out of your day.
We had a fantastic time in the city.....enjoy!