Chicago in December

There are tons of shops on State Street, right downtown, that you can find anywhere (H&M, Old Navy, etc.). Same goes for WaterTower Place.

There's the Christkindlmarkt, too, right at Daley Plaza that's fun! Great ornament shopping and potato pancakes and mulled wine in a boot.

If you want more unique shopping, check out this site: www.notfortourists.com/Overview.aspx/Chicago/Shopping

As far as restaurants go, just avoid chains. You can go to those anywhere. Chicago Pizza & Oven Grinder and Pequot's are always popular, and of course Uno's, Due's, Gino's and Giordano's for pizza. If you want a great Italian Beef sandwich, hit up Portillo's. Portillo's is also okay for a Chicago dog, but I prefer Superdawg or Gene & Jude's, but neither are city center.

Millenium Park is gorgeous and engaging. Don't miss the Art Institute. It's breathtaking. If you get to go, hit up Terzo Piano in the modern wing for lunch. Great views.

Fyi, Uno' s is a chain.

Don't miss Chriskindlmart - it's one of our holiday traditions. Across the street is Macys. Not the same as when it was Marshall Fields, but you can go see the big tree and if its your cup of tea - have lunch or dinner at the walnut room (which surrounds the massive tree).
Take a run over to Eataly - explore the shops or eat until your hearts content. There is a Shake Shack across the street from there too.

They sometimes have trolley cars that do tours of Michigan Avenue to see the lights and hit certain destinations. A lot of times they do groupons for the tours.

Great suggestions! The Christkindlmarket is really cool. You'll have to try the hot spiced wine and get a little souvenir mug. I'm actually not a huge fan and it makes me sneeze, but I always have to get some. One word of warning--whenever I've been there it is seriously crowded, as in really difficult to even walk or get up to the vendors. You can easily lose people in your group or small kids, so just be alert. 

Of all the museums, I love the Art Institute. It's world class and easily accessible--don't miss it! 

Eataly was another great suggestion. Dh and I went there several months back and made a meal out of salumi and cheeses at the standing restaurant, La Piazza. I've never seen anything like this place. You can spend hours there. There is just so much to see. 

I have to put in my vote for Portillo's. Their food is just excellent. I love the Italian beef, hotdogs, and their pasta sauce is actually quite amazing. I also recommend the chopped salad. Don't leave without having a piece of chocolate cake. They're known for it. 
If I may go off-topic for a minute, it's interesting how everyone's taste in hotdogs is different. Superdawg was mentioned earlier. It's a really cute place--your hotdog comes 'lounging' in a little box with fries. I like it OK, but their hotdogs are thicker than Portillo's, not as well seasoned (IMO), and they're skinless, so you don't get the 'snap' when you eat it. The toppings on this one are different, too. I actually really like them, but they're completely different than other Chicago-style hotdogs.  If I were you, OP, I'd try both!