Kansas City is the natural place to build a jazz museum. Jazz musicians from Charlie Parker to Pat Metheny hail from the KC area. The museum does not limit itself to local artists however. Rather, the goal is to provide an overview of jazz styles, eras, various geographic centers of jazz music and their significance.
There are lots of artifacts (including Charlie Parker's alto saxaphone), and interactive music-making activities. Mostly though, you have lots of listening booths and lots of commentary at hand that allow you to piece together Jazz's musical developments over the past 100 years. Imagine the listening booths at Borders, except there are lots more disks, and they are all the most important pieces in history.
The space is brand new and co-located with the Negro League Museum. The facility is located in the historic heart of Kansas City's African American community, and is experiencing a bit of a renaissance, with a couple of jazz clubs and nice restaurants springing up nearby. If you want to learn about Kansas City's past, this is as good a place to do it as any.