If you were to ask a Floridian what it is you can do in mid to late November in Chicago, specially a Floridian who has had the opportunity to go there many, many times, there is only one answer he can give you:
FREEZE YOUR A$$ OFF!!!
However, I would do Giordano's Deep Dish Pizza as Tom suggested.
As others have also said, the Hancock building is cool to go up to.
For me, it would be all about food. That city has awesome food to be had anywhere you turn to.