Kansas fan here. First off, I'm really looking forward to the matchup. Two very different styles going head to head--should be exciting.
davs50321 listed a lot of great places. I'd throw in Harry's Country Club in the River Market area. It's close to the Sprint Center and a short, free trolley ride away. Great patio, wild beer selection, fantastic music and ambiance. Also, when you're plowed at 3am and need grub, stop by Town Topic. It's a tiny hole in the wall diner near the arena and has great greasy burgers and is open 24 hours. Have a 'Truck Stop'. Deeeelicious way to spend 4,000 calories.
Westport is a really fantastic area with lots of excellent KC originals like McCoy's, Harry's Bar and Tables, Port Fonda, and the strangely iconic Kelly's. Because of this, I'd recommend spending time there as opposed to the Plaza or P&L. Power & Light is rather corporate, but they absolutely know how to host a basketball tournament. Also, there are quite a few bars within a couple of blocks of P&L that are local and have a lot more flavor. Extra Virgin (owned by a James Beard award winner), Record Bar, and the Cashew to name a few.
KU fans are typically pretty friendly people, so you should't get much grief wearing your Purdue gear around town or at the game. You'll probably get a few 'good luck's' from Missouri and K-State fans. Have fun in KC, enjoy the game, and let's all hope we're treated to a historic match.