If you want a central location, a block from the Harold Washington Library and the Chicago Art Institute on Michigan Ave., try Hostelling International's, Harris Family Hostel at 24 E. Congress Ave...For US$28 you get a dorm style room. Check out their virtual tour on their web site www.hichicago.org. Vey clean and safe for international travelers.
Don't forget breakfast at Lou Mitchell's at 565 W. Jackson, on the south side of Union Station.