Mcmoo - Hope you have a wonderful time here in Chicago. You have already gotten a lot of good advice - it would take you a month of Sundays to get around to all the different ends of the city that have music. One word of advice is to CALL FIRST, before going anywhere. Schedules get changed and the papers aren't always accurate or up to date.
There is a lot of "hidden music" around the city and suburbs - the coffeehouses are often local, neighborhood places that don't make the papers. Go to the Old Town School, if not first, really soon. It is the closest thing to a cultural center for folk music in town and the new facility on North Lincoln Avenue is a great place to hear music and find information (and inspiration).
Enjoy the city. The weather should be beautiful.
Bart