I have to go to Chicago next week, I’m arriving in the early afternoon, and have business south of the city the next morning. I’m staying on Michigan Ave, which I understand is right in the middle of the city.
What’s the must-see stuff downtown?
Any idea where on Michigan Avenue? A lot of the hotels are in the Magnificent Mile area. There’s lots of shopping there but little else of interest in winter.
I’d consider going to Second City to take in a show. There’s a good chance one of the performers will eventually be a recognizable star, and you can say you saw them before they were famous.
Depending where you are, grab a burger at the Billy Goat Tavern (the real one under Michigan Avenue near the Tribune Building). It’s the inspiration behind the SNL “Cheeseborger Cheeseborger” skits and is a Chicago institution.
Umm, I can think of a few non-shopping attractions on and right next to the MagMile. The view from the John Hancock building, which many consider superior to the Willis Tower view, is IMHO a must-see. If you don’t want to pay for “just” a view in the 94th-floor Observatory, go to the 96th-floor Signature Lounge for a drink and/or snack and enjoy slooooowly; the Signature Room restaurant on the 95th is underwhelming except for the view. 
If you can, go around dusk to see the day and night views.
There’s also the Museum of Contemporary Art, the Water Tower (the actual pre-Fire waterworks buildings on both side of Michigan Avenue, not the Water Tower Place mall), the Drake Hotel, the Fourth Presbyterian Church, and the area around the Michigan Avenue Bridge including the Tribune Tower and Wrigley Building.
If the weather doesn’t suck too bad 
a walk along Michigan Avenue from the bridge to Oak Street (where it ends by running into Lake Shore Drive) or vice versa is a nice architectural tour. A walk along Rush St. or Wabash Ave. (the next two streets west of Michigan Ave.) with peeks down the east-west streets reveals some of the surviving 19thCentury mansions interspersed among the more modern buildings. A couple of them sell Chicago’s famous deep-dish pizza. 
You are certainly centrally located in the heart of Chicago’s shopping district called the Magnificent Mile (aka Mag Mile) since it is about one mile from the river at the south end to the lake at the north end. If you are up for some holiday shopping this is an ideal place. IIRC the president of Dayton Hudson once called it the best shopping strip in the US (outpacing the likes of 5th Avenue and Rodeo Drive).
Within pretty easy striking distance (10 minute cab ride) are some major museums such as the Museum of Contemporary Art, the Art Institute (where all the old, famous paintings are), The Field Museum (natural history), the Shedd Aquarium and the Adler Planetarium (these last three are basically next to each other with the Art Institute a short cab ride away).
There is plenty more to do but that requires more zooming around the city and I am not sure how far afield you are comfortable going. So, for this, keeping you within about a 3x2 mile area along the lakefront.
For restaurants you are in the best part of the city. The Mag Mile is too touristy and overpriced for what you get but very nearby is the River North and West Loop neighborhoods that encompass some of Chicago’s best dining (including a 3-Michelin Star restaurant if you are wealthy). If you want recommendations for that there are plenty to be had.
Forgot to add:
The Mag Mile is pretty much all Michigan Avenue (although there are stores just a little off that strip too). So since you are on Michigan Ave. you are already there. For one day you could easily never leave that street and be happy.
The Museum of Contemporary Art is walkable. All the other museums are a cab ride. All the museums I listed are A-list kind of museums. Dunno if that is a thing so let’s just say they are world class museums. There are better in the world to be sure but these are no slouches (well, Adler Planetarium is a little meh but neat enough and it is right there with the Shed Aquarium and Field Museum so why not…Shedd is neat but no Seaworld).
As mentioned above the John Hancock, third (4th now?) tallest building in Chicago is walkable and worth a go. Drinks and food up there are meh and overpriced and service is shit but the views are the best to be had in the city as long as it is not in the clouds. You can also do the windows that tilt out. I have never done them but have been told they are a lot scarier than you might think.
I’ve heard the opposite - very underwhelming. The people I know who have done it said it’s not dissimilar from leaning your head against the window ala Ferris Bueller.
It also has the “David Bowie Is” exhibit going on right now, which is very cool, and will take up a couple hours.
Seconding both of these suggestions.
But buy tickets in advance, it’s been selling out early.
Around this time of year they have the German town Christkindlmarket going on. Its usually pretty neat to go walk around, get some warm wine and schnitzel. The vendors also have neat handmade gifts if you have anyone in mind who are hard to shop for.
The Macy’s (formerly Marshall Field’s) on State Street is a nice glitzy holiday experience, especially if you aren’t trying to actually buy something. Also, world famous Rush Street is right around the corner, in a zone called the Viagra Triangle (lots of older dudes with hot young dates).
Aw man, with all the very extremely delicious things to eat in Chicago, you all are recommending the Billy Goat? A fun experience while in line, for sure, but something good to eat, not so much. Get an Italian beef, the finest sandwich known to man. Eat a hot dog fer gawdsakes. Get a steak at Gene and Georgetti’s, or lamb chops, even better. Grab a cab and get some Polish food. Go to Harry Caray’s for some chicken Vesuvio. Do not, however, go to the Billy Goat.
Go to the Green Mile for a drink, catch some blues somewheres, Second City, enjoy the hell out of yourself. That is one fun city and I would live there in a hot minute except for winter.
I had a similar opportunity several years ago and at the time the one of the art museums had night hours. Check the museum sites for this info. The other museums closed at 5:00.