Heck, the OP needs to spend the whole day checking out the museums. I was home schooled as a kid and my mom would routinely take me to the Shedd, Museum of Science and Industry (further south on the LSD) and Adler Planetarium. I learned more in those four years then I have in the last ten years of traditional schooling.
Back to topic. Three things the OP needs to do.
ONE, find the Chicago Department of Revenues website. Check it weekly. Run your license plate through the ticket tracker every week, because the DoR are more vicious then Afghan warlords. Just because your car doesn't have an orange sticker doesn't mean you have no citations.... Ask me how I know.
Two unpaid tickets and the Denver Boot is sure to grace your car
Two, look up each of the museums I listed above, as each one has free days during the week. IIRC Thursdays are when admission to the Shedd and History Museum are free, although extra exhibits and 3D movies inside aren't free....nor is parking, but that's Chicago for ya.
Three, eat. While Chicago's known for pizza and whatnot, plenty of ethnic places exist which are fabulous eats. I know of a grand Thai place in a hotel on N Granville which serves the best Pad Thai you'll eat this side of the International Date line.