Where is your hotel? North Michigan Avenue is lighted beautifully for Christmas. In the downtown Macy's the window decorations should be something fun to see. It's not that far from Millennium Park.
If you are downtown, North Mich Ave. and Oak St. have the high end shopping. There is a high rise mall called Water Tower Place--not that unusual, but it's something most people visit. In the 500 block there is a mall that includes a
Nordstrom; 900 North Michigan Ave. has a vertical mall with a Bloomingdale's. Along the Avenue you'll find everything from Neiman Marcus, Saks, Louis Vuitton,
Gucci, Chanel, Bottega Veneta,
Coach, Tiffany, etc. to H&M, Macy's. Oak St. has
Prada, Hermes, Barney's, Tod's, and other high end designers.
If you want to visit some big malls, Skokie has Old Orchard; Oakbrook Mall west of Chicago has a lot of great stores. The largest mall is in Schaumburg (nw burbs)--Woodfield. Gurnee (n. of Chgo) has a large outlet mall (Gurnee Mills).
A lot depends on where you are staying and how much you like to shop.
There are too many great restaurants to list. Spiagga on N. Mich is Pres. and Michelle *****'s favorite restaurant. Bistro 110 is a casual but wonderful French restaurant near the old Water Tower. For casual but great food, the Peninsula Hotel has a street level cafe called Pierro Gourmet (I think that's the name) It's a block off Mich. Ave on Rush St. and you can eat there or get take out--fabulous meals, light fare and scrumptious desserts. When I don't feel like eating out, I pick up something to take back to my hotel room. You can't go wrong with any of the places to eat, really. It's just a matter of how much you want to spend.
I don't do nightlife or clubs so I'll leave that to someone else.
There is no predicting early December weather in Chicago. When we lived there it could be bitter cold with snow or in the 60's. If there is wind off the lake, it will be colder there than the *official* temperature at O'Hare airport which is actually in the suburbs. I would take a medium winter coat and pack some layers in case it's cold. Don't forget gloves, a scarf for your neck/face and something to cover your ears, just in case. Of course you can always buy those there but the sales tax is outrageous--over 10%. If you buy anything pricey, pay to have it shipped and you'll save on the sales tax.