Divvy bike share is a great option because there are pick-up/drop-off stations everywhere in the central parts of the city.

If it's too cold or if you don't feel like biking, then buy a 1- or 3- day travel card as soon as you arrive in the city. It will work even on train rides to/from airport. And it works in 24-hour increments from your first use.

The city is really easy to navigate, and you could spend an entire day (or just afternoon) walking around one of the neighborhoods. (Wrigleyville, e.g., is centered around Wrigley Field and is blocks from biking/jogging paths on the lake shore.)