The Chicago Public Library offers museum passes for the city's big museums. You often have to wait for one to be returned, but they are a great money saver on a fun outing. Also, visit other libraries that would have story time for toddlers: Lincolnwood, Evanston, Skokie, et cetera. Your daughter might want to run around a bit for these times, but if it is actually geared towards the 2 year old set, the leaders should be used to it!
Chicago Park District offers classes at very reasonable fees. Just be sure to register on the the first day because spots fill up very quickly!
You could also try the Exploratorium in Skokie; it's at the park on Oakton and Skokie Boulevard. There's a fee if you not live in Skokie.
Someone else mentioned Kidwinks.com--that's a great resource. There is also Chicago Kids and Time Out Chicago Kids.
And though I hate the mall, I have brought my monkey to the mall just to run around. Northbrook Court has a nice kids' play area.
Have fun!!