One of my favorite things to do in the spring and summer is visit Lincoln Park Zoo on Chicago's north side. The gates to the zoo open at 7AM and I usually try to sneak in there before work (before the "official" opening at 9AM). If you can make it in that window, there are very few people around, allowing for plenty of peaceful browsing and walks around the zoo grounds, pond, and nature boardwalk areas. You'll also beat the loud crowds and mid-day heat, so the animals are much more likely to be out and about. Be aware that the vending, cafe, and indoor animal viewing areas will not be accessible until the official open.
The best part about Lincoln Park Zoo is that it is FREE to enter — for anyone. You wouldn't assume this from the quality, however. The exhibits and enclosures are large and clean. The grounds are gorgeous and well maintained, with flowers and foliage filling any empty areas. The staff is quite friendly and very knowledgable. The zoo offers plenty of information on the animals, upcoming exhibits, etc. and offers many programs and events to engage the public, children and adults alike.
Soon the zoo will unveil a large new exhibit that has been under construction (near the Kovler sea lion pool) for some time. The Regenstein Macaque Forest will open in Fall, 2014 and promises to be a natural and state-of-the-art facility for the Japanese primate. I'm looking forward to visiting again when it launches!