I am from Chicago, so I would be happy to answer any of the questions you have. I personally would stay at either the Holiday Inn Chicago O'Hare area or the Marriott Springhill Suites. Both of these are near O'hare airport, but far enough away that they offer free parking. Both are close to the city's blue line, which is a subway that will take you right into the hear of the city. To get to American Girl Place, you may have to take a bus off of the train, or transfer to another train. Either way, both are easy to do. The rates for both hotels seem to be in the $100 range. There are also loads of restaurants in this area.
Someone advised to stay near the Metra line. I don't know that I would necessarily agree with that. The reason is because, while Metra is a great option for commuters, unless you are staying literally right next to the line, you will have to park at the station. That adds money, but more importantly, it may be impossible to find daily spots at the parking lot. In addition to that, you will still likely have to use the subway/buses anyway as the Metra stations are closer to the downtown area, not necessarily the "tourist" area. You would then need both metra and CTA fares, and that could add up. There are both one day and three day CTA cards that allow you unlimited access to buses and subway/elevated trains for the length of pass. I believe those can be purchased at Jewel and Dominick's grocery stores when you arrive.
One definite recommendation is the Wendella river or river/lake cruise. Both are really awesome tours. We like the river/lake, as you go into the Locks.
If you have any further questions, I would be happy to answer them.