Hit the sidewalks
Many Chicago apartments are seemingly not advertised; instead, the building owner places a flyer in the door of the building describing the apartment available. If you find a neighborhood that you like, walk down the streets and look for these flyers.
This is what people told me when I was looking, but I didn't really want to do that. It takes alot of time. But this advice is true. I always see "apartment available signs" on doors in Wrigleyville/Lakeview.