A third-generation Chicagoan here though I haven't been back there in many years now. I do keep up with some developments there, and I understand that the parks are still here.

Lincoln Park is a great park (north side) and has two splendid ponds or lagoons.

It also has this Lily Pool (which I think was called the Zoorookery years ago--looks like the place I remember):

http://www.chicagoparkdistrict.com/i....natureOasis06

Jackson Park on the south side has a wooded island, just south of the Museum of Science and Industry. The island is a fairly sizeable chunk of nature kept free of anything manmade. You can see many birds there if you're interested in birds.

This tells about it and there's a photo:
http://www.chicagoparkdistrict.com/i....natureOasis16

Somebody mentioned the Morton Arboretum--another great place for nature though it's a distance to travel.