There's some legendary BBQ in KC. If you have the time, and you like that kind of thing, hit any one of the top 5 spots in KC and you can't go wrong.
When you get to campus, I would second @ku4bob and @BShark -- the Natural History Museum has some great exhibits (and family ties for me). It's in Dyche Hall which is next door to the Union where, in the basement, you can go bowling at the Jay Bowl... And there's the Spencer Art Museum below the Union and across the street.
All of that is pretty close to each other on one side of campus. The Fieldhouse, and the DeBruce Center (which is attached) is across campus.
I can't think of many other things that are set up as attractions for visitors... Some might say The Wheel is must see.. I assume it's still there. Not sure about many other bars, like the Hawk... Those are/were just off campus..
I'm sure there are some other hidden gems on campus, but I think I took them for granted and have forgotten.