Your number one priority should be Chicago style deep dish pizza. Lou Malnati's has multiple locations and is a great place to try it, but there are several others in town as well. Also Italian Beef sandwiches for food. Al's is supposed to be the original, but again there should be several good places to get some. Just ask your hotel what's good near you for both.
For things to do definitely go to the Navy Pier area. Plenty of good shopping, restaurants, and things to do there. There are also a few places there that offer boat tours. It'd be a great way to see the city. You may want to look into booking in advance for those.
Also Millennium Park is great for a nice day (if you get one in January). It has the famous Cloud Gate and Crown Fountain. There is also an ice skating rink there.
Aside from that, plenty of museums to enjoy like others have said. And also +1 for Bulls/Blackhawks game if you have the extra money. I would go Blackhawks personally - hockey live is boss and Blackhawks should be much better than the Bulls - but either would be very entertaining.
It's a lovely city, enjoy mate.