Chicago is one of the few American cities where you genuinely do not need a car. The "L" elevated train connects the airports, the Loop, and most major neighborhoods, and a single-ride fare covers the whole system. CTA buses fill in the gaps, though they can be unpredictable. Walking is the best way to experience individual neighborhoods -- the city is flat and the grid system makes navigation simple.
The Blue Line runs 24 hours between O'Hare and downtown, making it the cheapest airport transfer in the city. Midway is served by the Orange Line. Metra commuter trains are useful for day trips to suburbs like Naperville or Evanston. Taxis and rideshares are plentiful but expensive during rush hour. For the lakefront, renting a bike through Divvy, the city's bike-share system, is hard to beat.