We just have an 18 month old, and will be homeschooling, and traveling is definitely on my future agenda. However, I noticed you mentioned Chicago, we live in the suburbs of Chicago and are also natives of the city, so I thought I would tell you some great places to go for cultural experiences.
There are the popular museums by Sollider Field, which include: Shedd Aquarium, Planetarium, and the Field Museum.
The Museum of Science and Industry is about 15 miles south of downtown Chicago and is great for all ages.
During the Summer Millenium Park does free activities all day long for kids and adults everyday including weekends.
There are also many ethnic museums such as DuSable, Museum of Mexican Art and Polish Museum of America.
The History museum is also a great place as well as our two staple art museums which are Art Institute and Museum of Contemporary Art.
You can do many tours in the city, with just an ipod/ipad/iphone, most of them are free downloads in iTunes. There are many neighborhood tours as well as architecture tours.
There is so much to do in Chicago, you have to have an agenda and a budget! Good luck on your travels!