R.M.
We have a membership to the Aquarium and my 21 mo old LOVES it. We go early in the morning when it opens, around 9:00 before others get there and run around, see the animals, have a snack by the penguins, run around on the ramps, etc.
There are also so many park district playgrounds to visit; some with sand, some with water features, some with soft surfaces, etc. http://www.chicagoparkdistrict.com/ has information.
We also love to go to Belmont Harbor and feed the ducks old bread.
Good luck with your little one!