There is hostel on Wabash and congress.
your best bet is to get a hostel in Chicago in the downtown area. It could cost you anywhere fro $14.00 per night in a dorm to $50 a night single room.Try this website www.hostels.com and you get great deals and then call the hostel and tell them you are staying for 3 months and they might even offer you a more cheaper price.
See if a student from Columbia or Roosevelt has an apartment they need to sublease for the spring semester. Otherwise, I would just go with the hostel.