I grew up in Wichita, Kansas, about 3 hours south of KC. You definitely want to get some BBQ. It will be some of the best you can possibly have, and Lee is right about Arthur Bryant's.
Weather is a real crap shoot. Could be snowing, could be raining, could be 60 degrees F. It's a little early for tornado season, but you could still get a might thunderstorm if you're lucky. They are very impressive.
Been a while since I'v been in old KCMo, but the Nelson Art Museum is very good, check out the Westport section, should be some good music and bars. Blues and Jazz. Don't bother going across the river to Kansas City, Kansas...
And, on an historical note: Kansas City can claim one of America's great contributions to international sports car racing, Masten Gregory. If you're not familiar with him (really? can that be?) here's link on him:
http://www.geocities.com/mastoidfan/mg.htmlPeople should be pretty friendly. Us mid-westerners are funny that way. Yes it can be very conservative politics wise, but that doesn't mean you can't find smart people with realistic views of the world, and dare I say... liberal agendas?
John