I'm from there and if I were you I'd drive right by Chicago and wave at it as you head to Wisconsin. Nothing really there to see and your kids would be bored to tears if you took in any of the cultural sights you might like.But then again you won't be able to go downtown with your RV and there are no close by CG's. There is one in Zion on the lake but it's nothing to write home about.
Take the extra time and spend it all in Wisconsin. Endless stuff to do there, CG facilities abound and the scenery is just down right spectacular. Stay in small towns there is so much activities planned all summer especially during Dairy Month. Each town a big farm sponsors Dairy month. You get to really see how a diary farm operates and all of them have 6 foot frying pan and serve up breakfast in it! I try and make one every year. Lake Geneva, Door County good spots too.
The Wisconsin State Fair in West Allis (right outside Milwaukee) is the BEST fair of all the states. They have a full hookup CG on site. It's like no other fair you have been to. The kids will love you for the rest of your life if you take them to that! :C