I believe that other than the Navy Pier trolley, the Chicago website says that the other free summer trolleys have been discontinued :-(
Also, be sure to not hype up the beach too much - we have been having beach closings on some summer days (especially later in the summer) and wouldn't want her to be disappointed.
Lincoln Park Zoo is FREE! Although, in August be sure to check the weather/heat index - some days are just miserable sticky.
Stop by the Chicago cultural center - they have tons of info. on what's happening in town (with brochures & maps) - plus, you can pick up discount coupons and free day info. too. Check to see when the air and water show is also in relation to your visit -- once you get closer, the Chicago website should have a cultural events calender pretty well defined - summer months bring Tues. night movies in the park (free), Thurs/Sat orchestral concerts in the park (also free)
Oh, and Chicago has a Rainforest Cafe, which some kids also like to eat at.