Museums: I'd second the Federal Reserve Museum. It was really neat seeing not only the history but millions of dollars going on by on pallets too, lol. Nelson Atkins is a must, and these two suggestions are from non-museum going people.
Warm weather: If you are there during the summer the farmers market is fun, I think there is Shakespear in the park somewhere.
2 Unique sports: Pickleball is becoming quite popular there, Chicken and Pickle is a restaurant/bar with indoor and outdoor pickleball courts and paddle rentals. A big facebook group (10,000+) has an annual meetup in KC, with this year's being in some big new sports complex. The second would be axe throwing, although I guess most major cities have these popping up now.
BBQ: For BBQ I know Arthur Bryant's is the "tourists" choice, however they have the best hand-cut french fries imo anywhere. We split a turkey sandwich, portions are large. I'd also second Jack Stack, Martin City is the original but the other two locations are also great (but a different, fancier atmosphere). Joe's Kansas City bbq (formerly Oklahoma Joe's) has never, ever let us down either.
Stay: If you like the urban feel, downtown I guess. Country Club Plaza is a big shopping district with nice lights around Christmas. But we tend to try to stay in Olathe or Overland Park whenever possible. Prarie Fire district is a newer area with some more shops, pinstripes for a unique bowling experience, and some nice restaurants.
OP, just in case you get tired of BBQ but are still hungry, we could debate the best Mexican place in town. That’s almost as contentious as the best BBQ.
Umm, do tell. We have been going to KC as a weekend getaway for almost 20 years now and mostly do BBQ or somewhat Italian (Cinzetis, and Jaspers would be real Italian I guess). Recently we have been enjoying a few different Jose Pepper Cactus grill locations, as well as Chuy's in Olathe. Are there more Southwest style mexican places around?