If you want to minimize your time in Chicago, use a rental agency. The primary advantage is that they have immediate access to all apartments in their inventory so you don't have to try to coordinate showings with a dozen different people, half of whom may or may not return your calls at their own leisure, completely unconcerned about your time schedule. The standard operating procedure is that their services are free to the tenant; they collect their commission from the landlord. I recommend
The Apartment People, particularly their Lakeview office. They can be a bit snooty, but they have a HUGE inventory of rental stock. If you're going to be in town starting on the 14th, contact them in about, say, NOW, to set up an appointment.
I don't recommend the "Drive around and look for signs" approach as your primary search method, but there's nothing wrong with doing that in addition to other methods. Be aware that "For Rent" signs can be misleading. Many of them are actually permanently attached to the building. Such signs usually mean the building is run by a management company and they're just providing general contact info; they may not actually have any units available in the building with the "For Rent" sign. Usually the generic black dime-store signs with "FOR RENT" in bright orange lettering are legit, especially if they have hand-written info in the white info box.