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Its pretty easy getting to all of these places via public transportation. The CTA (the "El") runs trains from each airport into the Loop (the center of the city). The train is pretty well marked at each airport and there will be staff at the stations that can assist you further. The Blue line is from O'Hare and the Orange line is from Midway.

Once in the Loop, you will have to change trains to get to your hotel (if staying in River North, which is the focus of the tourist area and has tons of entertainment/dining options) you'll most likely be transferring to the Red line.

To get to Evanston, you'll have to either take the Red line north to the end and then transfer to the Purple line, or if you're going during weekday rush hour, you can take the Purple line from downtown. The campus is a relatively short walk from the Purple line stations.

To get to the Univ of Chgo, you'll be taking the Green line south and again taking a relatively short walk.

Check out the CTA's website at www.transitchicago.com. One of its features is the trip planner which will give you step-by-step directions to get from any address in the city to any other address in the city and lets you plan by fastest route, shortest walking route, etc.