Books have been written on this topic - big ones. I lived there and visit often. My top pics -
Food-
Ruth's Chris Steaks on Dearborn - yeah it's a chain, but a damn good one. I like it better than the Chop House and Gibson's, but they're all three very good. Make sure to get reservations.
Marai for Sushi on west Division in Wicker Park (just west of Rush street by a couple of miles). Best sushi I've had - anywhere. Cool decor. Try the saketini. So what if it sounds gay - it tastes great!
Harry Carrey on Dearborn for lunch. It's iconic.
RA sushi on Rush - again a chain, but good and very cheap. Decent Saki and hot servers.
Gino's on Wells - much better than Pizza Uno
Drinks - too many to list but in that area I like-
Wimpy's Hunt Club on State. Right on Staet and Rush, it's a fun area to people watch, if not a bit touristy. Wimpy's has Blue Moon beer instaed of that Goose Island crap served everywhere else.
Excaliber, but only late and on weekends, otherwise it's size makes it very apparent how dead it is. When it's busy, it's huge fun. Practice "not looking" now.
Shopping -
All of Michigan Ave. Nordstroms mall is close to the Omni and excellent. The kids will love the water tower - dozens of shops. I like the Burberry store. Bloomingdales, Tiffanys, etc., etc.
Culture - It should be required to pay admission to these 3 things to even be allowed into Chicago -
The Art Institue of Chicago, just because it was featured on
Ferris Bueller's day Off....or if your even remotely interested in fabulous, historic works of art. Check out the courtyard area just north of the building (attached pic)
Field Museum. Again, iconic
Shedd Aquarium. A terrible shame that the oceanarium is closed while your visiting, but it's still cool.
In addition to those three maybe check out Chinatown. Very cool, but it will be a chilly walk. I would plan it for a short lunch trip. Best visited in summer.
Transport -
All of this is very close by cab and cabs are cheap in Chicago. Just wave at one with the light on. Hard to find getting out of Chinatown though so take the subway north to get back downtown.
The subways are excellent, if not seedy. If you are good at navigating subways, go for it. Otherwise stick to cabs as a wrong subway ride can put you were you don't want to be very fast.
Driving isn't so bad, but parking is difficult and expensive. A jaunt up Lakeshore is a nice diversion.
Walking Michigan is great. Cut over to Rush and basically check out the side streets (Elm, Maple, other tree named streets) to see upscale Chicago living. I love the architecture.
Last piece of advice - BRING A CAMERA!