For seats, we sit on the 35 yard line about halfway up the upper deck, and my dad sits right at the side of the endzone 12 rows off the field. I prefer our seats to my dad's, because I can watch plays develop. My dad is so close I end up watching the game through the jumbotron whenever I sit down there. I'd sideline in the lower part of the upper deck is the way to go. Also, the higher rows of the lower level have the overhang of the club level above them, so you'd be safe in case of any bad weather.
I highly recommend the stadium tour. You'll get to see parts of Arrowhead that you'd never get to see otherwise, and learn a lot about the history of the Chiefs and the AFC in general (since Lamar Hunt helped found it). It also starts and ends in the Chiefs store, so you'll be able to do some shopping there as well.
My favorite barbeque in KC is Arthur's and KC Joe's. Many will have differing opinions, so take that for what it's worth. If you enjoy some good bars and good food, you should definitely check out the Power & Light District and Westport. Any local art museum in just about any city is interesting if you're into whatever exhibit they have going on. Union Station usually has some pretty cool photo ops, as well as being an interesting place to visit.
I'm a few hours from KC, so I'm not necessarily a local. I'd like to think I have a good idea of what it's like to "visit" there.
