Jack Stat's Oklahoma Joe's Kansas City BBQ is amazing. It's no Texas BBQ, but out of all the regional BBQ's it's my second favorite.
eat Oklahoma Joes and arthur bryants, stock up on gates bbq sauce and drink as much boulevard beer as possible.
Also if your in your mid 20s going to westport for bars/clubs. although they do lots of dui checkpoints so cab it up or walk.
I went to Mizzou and know KC well. P&L is definitely the spot to be at night. I'm actually making the same trip, albeit just in KC Friday night. Driving to Columbia on Saturday for Florida/Mizzou, then back to KC Sunday morning for Texans/Chiefs. I always liked McFadden's, and we learned during March Madness that that's where Marshall Henderson went to party. But the best thing to do is stay flexible and walk around a bit -- the scene varies from night to night. I'll also second the Oklahoma Joe's recommendation. Granted, it's a hole in the wall connected to a gas station. But as far as a lunch spot goes, that's as good as it gets. Best BBQ I had up there.
I went and tried Oklahoma Joe's tonight and I must say the food was amazing! Definitely a must try place when your in town. There's also more than one location as well.