Chicago Airports, links to both of Chicago's metropolitan airports... O'Hare and Midway. Gary-Chicago
Metra, regional commuter rail system serving multiple downtown stations and all major suburbs
CTA, Chicago's public bus & rail system, serving the city and some neighboring suburbs
Amtrak, national passenger railway, to Chicago Union Station.
Much of Chicago's cultural life is focused downtown, on the northwest side, and the north side. If you understand the city's transport system, you can easily see it all on the cheap. It may take some planning and time to reach your destination, but it can be done.
Major streets typically have their own bus lines, and rapid transit lines (a.k.a. "the El") runs to and from major destinations. The El system runs on a hub-and-spokes scheme, part subway, part elevated electric train. Most lines connect with each other downtown, some in outlying areas, too. All El lines use the same basic coaches.
Some El lines and many arterial bus lines run 24 hours a day; however, service during late hours ("owl service" as it's called) can be very infrequent, so consider a taxi after 11:00 PM unless you're absolutely broke. Trains and busses, while messy by other cities' standards, are fairly safe, day or night.
Neighborhoods in and near the city center (which we call "The Loop") are generally safer at night than those inland or further out. For example, Wicker Park's recent affluence looks nice in tourist brochures, but it's still a bit rough when you know it well. However, savvy travellers (and the locals) know that the real Chicago lives nowhere near downtown. Go inland for adventure and a taste of the authentic city, away from the tourist trap restaurants and convention centers. Choice neighborhoods to explore: Lakeview, Andersonville and Edgewater (North Side); Hyde Park, Kenwood, Bronzeville, and Beverly (South Side); Chinatown, Pilsen and Little Village (Southwest Side); Wicker Park and Logan Square (Northwest Side).
O'Hare Airport is served by the CTA Blue Line El, through the northwest side of town. That same line serves our flagship venue, Center Portion, at the California station. Midway Airport is served by the CTA Orange Line El, through the southwest side. Nearly all commercial flights arrive through these two airports. Taxi or limo service to the Loop from the airports runs anywhere from $20 upward; on the El, it's less expensive... just a word to the wise.
Domestic airlines that offer budget flights tend to serve Midway, while O'Hare is the de facto international port of entry. Amtrak serves Chicago from the entire USA, but expect to measure travel times to Chicago in days rather than hours; high-speed rail has not yet reached our city.
You can purchase CTA passes from vending machines at all El stations and at larger food stores. These electronic passes function like debit cards. You can add value to them, and they are all but required to board trains and busses.
For transport around the larger metropolitan region, Metra cannot be beat. It is low-cost, on-time, clean, safe, and quite likely the best commuter rail system in the US. Europeans should not confuse our "Metra" for what they typically think of as "the Metro". Metra is our regional surface rail system, and not a subway. Europeans may also feel that our trains are infrequent, but for a country where the Car is King, these trains serve as a genuine alternative to driving. Amtrak shares Union Station downtown with several Metra lines, so interchange is fairly easy. If you choose a B&B or hotel in the Chicago suburbs, make sure it's walking distance to a Metra station.