I see lots of layering recommendations, good. I might add to get yourself a couple packs of hand warmers. The kinds that warm up when exposed to air. You can open one and put it nearer an inner pocket amidst your layers of cloths. It can keep your whole body warm. Good for when the jarring cold is even more jarring than you'd planned for ;-)

Shedd Aquarium is right downtown on the lake front and lots of fun. Less than a block away is the Field Museum which you can easily spend a day wandering through. Near both is the Adler Planetarium if you look for that sort of thing.

Just south of the bean (cloudgate :-p ) is the Chicago Art Institute which is way larger than it looks (to me). Regardless of what artist is showing, the institute has large displays of art ancient to modern.

There are also a few musicals playing. Hamilton is scheduled to end in Dec. but it might be extended. I'll help you out and go see it to increase their audience counts ;-)

Since it's February and you may want to check out the underground, look into the pedway https://en.wikipedia.org/wiki/Chicago_Pedway Maybe not for the faint of heart? You can walk from city hall to the train station under Randolph & Michigan on the corner of the bean. Fair warning though, the Chicago underground is far more massive than these maps show. Look up the Chicago Pedway sign. When you see it, you'll always see it ;-) Keep to the busy areas and times as it will be much harder to get lost. To give you an idea, the land under Millennium Park is a multi-level parking garage with various walking tunnels, train tunnels and a theater (yes, on Randolph :-p Lobby level is technically in the underground though). That's not to mention the underground streets.

I used to work in the Prudential building which is part of the pedway. Can you tell I miss being down there? ;-)