When I'm looking for a place, I always go for a B&B, as I think they offer the best value. Hostels are cheap but unwelcoming, hotels are very expensive for what they offer, but B&B's are comfortable and not too pricey. Very often, you'll pay less than you would in a hotel for a luxurious room in a private apartment. In Chicago, I stayed at the House 5863 B&B, in the residential area of Andersonville. It's not too central, but as in many American cities, the downtown area is just for skyscrapers and offices.
For $120 a night we had a double room with all the amenities: a large bed, air conditioning, flat screen TV, and wireless internet.