Where are you guys staying?
The Boulevard tour always gets high marks. I haven't been for about 7 years. The brewery has expanded exponentially since then, but the tour is still outstanding. If you like heavier beer, try some of Boulevard's Smokestack series. They have a variety of styles. They're sold in wine bottles, and they're around 12% alcohol.
You should also visit the Negro Leagues Baseball Museum. http://www.nlbm.com/
Power and Light is fun, but kind of corporate. If you go there, visit the Flying Saucer for beer. Any beer. They probably have it. You can also visit the College Basketball Hall of Fame, located at the Sprint Center.
South of Power and Light is Westport. Older, locally-owned watering holes. Kind of a young, bar-hopping crowd. If you go there, visit McCoy's Public House. They have their own microbrewery. The Comedy City improv theater is at the Westport Flea Market -- they put on a quality show.
Just south of Westport is the Plaza. It's Kansas City's centerpiece, filled with high-end restaurants and stores, so be sure to visit. The Nelson-Atkins art museum is in that area as well. Too many good bars to mention, but O'Dowd's Little Dublin is a personal favorite. Enjoy a rooftop beer if the weather is nice (it won't be, though).
I'm not a big fan of the Legends area. It's very corporate, with chain restaurants and outlet shopping. However, the new soccer stadium there is very cool, and the Schlitterbahn water park is apparently great, even though some of it is still under construction. The main stand-up comedy club (Stanford's) is also at Legends.
As for BBQ, the big guns are Arthur Bryant's, Oklahoma Joe's, and Fiorella's Jack's Stack. Go to the Arthur Bryant's downtown -- that's the original one, and it's the best. There is one at the Legends, and it is downright embarrassing. Oklahoma Joe's has a midtown restaurant located in a gas station (well, it's a full-sized restaurant that happens to share space with a gas station/convenience store). You should visit it, but go at about 1 pm. Don't try to go around the regular lunch time, as you will be waiting in line outside in the heat for probably 20 minutes.
Those two are excellent, authentic BBQ. Jack's Stack is BBQ fine dining. And it's worth the price, IMO. Visit their plaza location.
If you want a change of pace from BBQ, you can't go wrong at any restaurant on the Plaza or in Westport.
If you have any other questions, just post them here or shoot me a PM. I'm glad to offer my opinions.