For food, consider Lidia’s (Italian), Arthur Bryants or Gates (BBQ).
For sites, the Science City at Union Station, Nelson Atkins museum and the KC Jazz museum. Royals baseball tickets are going to be cheap if not free ... might consider a game.
Actually that's why I'll be in town. I'm a Giants fan and the Giants and the Royals are playing a three game weekend series this weekend. I was kind of amazed that I was able to get very good seats on short notice.
I do want to give Arthur Bryant's a try, but if there's somewhere else that's better that locals recommend, I'll give it a shot.