Hostelling International-Chicago: The best hostel in Chicago is located in the Loop, walking distance from...everything. Rooms are most likely to be available in the summer, since the hostel serves as a dorm for Columbia College during the school year; but it is worth a try year-round. Rooms are stark but clean, and cost $34-44.
The Palmer House Hilton: Comfortable rooms, a spectacularly gilded lobby, and the perfect location -- close walking distance from the Art Institute, the Symphony Center, and Grant Park. There is also a chance that you could get a room at the Palmer House for around $100 (before the 14.9% hotel tax, which will affect you wherever you stay). Prices do range up into the low $200s, which is still modest in comparison to many hotels in this area.
The Silversmith: Another beautiful hotel in the Loop area. Rooms range from $109-319.
Hotel Burnham: Located in the architecturally significant Reliance Building, which was built in the 1890s. The Hotel Burnham is also well-placed for walking to the parks and museums. Room rates are a little more expensive than the Silversmith, at $169-399 a night.