The bad ‘hoods are on the west and south sides, but well away from the tourist haunts. The Loop, Gold Coast and the Magnificent Mile shopping strip on Michigan Avenue are all fine, day and night. Also safe are Lakeview and Lincoln Park districts.
If you’re heading to the University of Chicago and to the Frank Lloyd Wright home in Hyde Park, don’t stray south into neighbouring Woodlawn, or a few blocks west into Englewood.
If you’re using the “L” (elevated train) make sure you get on the right train, indicated by the ‘colour’ of the line it runs. Many lines run through the same station, get on the wrong one and you’ll be in the bad part of town before you know it. Streets around the Howard Red Line stop and the Wilson Red Line stop are not places you want to be.
We have a few more tips about safety here: http://safety.worldnomads.com/USA/69319/Bad-Neighborhoods-USA-Crime
Hope that helps. Phil at the safety hub about 6 years ago