Places I've been to, or have been recommended.
If you are interested in public art the Chicago Public Art Group has put them all on a map which can be found here: http://www.cpag.net/home/map.html
History Museum · Lincoln Park · 61 tips and reviews
Catriona Hunter: The section on the history of the city is really interesting. They have some objects that survived the Great Fire (well, survived is a relative term)
Catriona Hunter: Special exhibit tickets sell out. So get there early if you really want to see something. If you are in a group, book your tickets together to ensure you get the same timeslot.
Catriona Hunter: The only WWII German U-boat in the USA. To actually get on the U-boat requires an extra ticket above general admission. Absolutely fascinating.
Burnham Park (btwn Roosevelt Rd & 18th Dr), Chicago, IL
Other Great Outdoors · 29 tips and reviews
Catriona Hunter: Area containing the Field museum, the aquarium and the planetarium. Some good views of the city, especially from just outside the planetarium.
Catriona Hunter: The Ferris wheel is open all year, but the other rides close in the winter. However if you buy a 5-ride ticket it is valid for a year.
233 S Wacker Dr (btwn Adams St & Jackson Blvd), Chicago, IL
Scenic Lookout · The Loop · 392 tips and reviews
Catriona Hunter: Buy tickets online in advance to skip the line. Can see four different states on a clear day: Illinois, Indiana, Michigan and Wisconsin
Catriona Hunter: Best French toast in the city. The choc-chip, banana and bacon pancakes aren't bad either. Also has a vending machine where you can get a branded pen for 25cent :)