Chicago Architecture Tour is a must. More of a summer thing but we have Indian summers out here so you should be good in October.
MIllennium Park and the Chicago Art Institute are right next to each other, they're great. Chicago Athletic Association hotel is right across the street. Have a drink and or a snack/lunch in the lobby on the second floor (it has a Shining Hotel feel.) I've vegged out in there for the whole day in the winter....Giant fireplaces, with old school bars, a gameroom and the most comfortable chairs and couches around (you can order right from the couches and chairs and get a pretty damn good Caesar salad with anchovies and a really good fried chicken sandwich. Actually tour the whole building if you can, the Cherry Circle Room and rooftop is supposed to be cool but usually a line for rooftop....
Walk over to the Palmer House Hotel and have a drink in the lobby, it's my favorite lobby anywhere. Miller's Pub is right down the street and a classic Chicago pub, one of my favorites.
The Green Mill is a classic, Al Capone's old hangout but that would be a hike if you're staying downtown. A couple of total dives downtown are Rossi's and Snickers, Larry Bird would hangout at Snickers when he was in town with the Pacers. Old Town Ale House in Old Town by Second City. It might be a little smelly and cash only but every comedian you can think of hung out there/still does and has their picture on the wall.
Walk around The Gold Coast and look at the Architecture. You could start at the Old Playboy Mansion and then just walk around all those streets, some amazing Architecture. They have one of those Restoration Hardware anchors over there and it's like a museum inside and out. Your wife would probably like having lunch in the 3 Arts Cafe atrium in there.
A lot of people like the Signature Room at the top of the Hancock for the 360 degree views of the city. I wouldn't wait in any line for it though, the view is great but then you'll be buying way overpiced drinks and food. Gibson's is a classic for steaks and people watching.
I love French restaurants, it's my favorite cuisine when having a nice meal and 4 of my favorites have all closed (Bistro Zinc, Cochon Volant, La Sardine, Kiki's Bistro.) Le Bouchon in my neighborhood Bucktown is still around and has always been really good...same owner as La Sardine, he sadly passed away a few years ago. The Bristol down the street is also really good (owner was carjacked and shot right outside the restaurant) but is fine now. Rich folks in my neighborhood got together because of all the carjackings and muggings and hired private security for the neighborhood which seems to be working. If you make it this way go the Map Room, it's one of my locals and has 26 beers you're unlikely to find on tap anywhere else and something like 200+ beers on hand at all times.
Some other favorite restaurants of mine are Tango Sur, Osteria Via Stato, The Publican. You can't really go wrong with Frontera Grill (moderate) and Topolobompo (expensive) Rick Bayless places are classics but there's more inventive higher end Mexican places now most of which I haven't been to. I can't really think of other higher end Mexican restaurants (I usually go to little grocery store kitchens for Mexican) but get Mexican. We probably do it better than anyone....
Stephanie Izzard's restaurants are all really popular and incredibly hard to get into. Some of these restaurants you really have to make reservations far ahead of time. My friend was a chef at Nico Osteria, owned by Paul Kahan. Same owner as The Publican it's known for it's crudo. Only went once when he worked there, it's really good but really expensive.
River North and the West Loop have so many restaurants and you really can't go wrong with any of them. A lot of cool bars and restaurants in Logan Square, it's our big young hipster area, used to be Wicker Park.
I always tell people our restaurants are comparable to Manhattan prices, same with downtown drinks at the fancier cocktail places (I avoid all that stuff like the plague) our hotels tend to be way cheaper.
If you haven't made a hotel reservation yet, I would do the Palmer House. It's enormous, packed with history and I just love being in the place. It's also insanely inexpensive for what you get. Scratch that, just looked it up and it's way more expensive than it used to be. All the hotels are trying to make their money back now and are short staffed.
I wouldn't bother with Italian beefs, deep dish, Chicago dogs, or breaded steak sandwiches. They're all good but you probably won't he near the places who do them the best. Unless you want to go to Portillo's. It's a chain but you'll get a good Chicago dog or a good Italian beef there, get the combo with the smoked sausage link and giardinera.
Haven't been to Second City in many years, not a huge fan of improv but that's a good suggestion. I used to hang out with a lot of those guys and Improv Olympic guys. Check on concert venues and comedy venues, there might be a musician or stand up you really like who is playing then, there's a lot of venues for both. Steppenwolf theater (John Mahoney, Traci Letts) has a great reputation for plays. We lost Blues on Halsted due to the Pandemic, it was the best but Kingston Mines and Buddy Guy's have legit performers every night.