E.B.
Here are my ideas:
Kohl Children's Museum in Glenview (EXCELLENT)
Lincoln Park Zoo (in the city and it's free)
Brookfield Zoo (not free, but a wonderful zoo)
Cosley Animal Zoo in Wheaton
Beaches all along Lake Michigan
Wagner Farm in Glenview
Peggy Notabart Nature Museum, across the street from LP Zoo
Pirates Cove in Elk Grove Village
Kiddieland in Melrose Park
Some of these places (Wagner Farm, Cosley Zoo) aren't full-day activities, but they're either free or inexpensive and a nice, short visit for kids with nice, short attention spans :) You could do the Kohl Children's Museum, then have lunch, and then see the Wagner Farm - they're within a mile of each other.
If you have any questions or want some more ideas, let me know!