There are plenty of things to do in KC!
Someone mentioned the fountains at Crown Center, which is a ton of fun. It's probably not more than a 10 minute drive from downtown. Also at Crown Center is Kaleidoscope, which is put on by Hallmark, and is free. I used to do this when I was a kid. I am not sure how old your DD is, but my nieces (7 and 8) loved it. you can check it out at at hallmarkkaleidoscope.com/. There is also a free
Lego exhibit going on past Labor day at Crown Center (crowncenter.com). Science City at Union Station is very cool too. There is a Narnia Exhibit there right now and I think there is an IMAX. Union Station is only a couple blocks from Crown Center and the WWI Museum (I saw someone else already mention that), so it's all within walking distance. Check the visitkc.com website too... there are a lot of two for one specials, including for Union Station and Science City.
Someone mentioned the Country Club Plaza; which is neat to walk around. Buca di Beppo's is an awesome family style Italian Place, but there is also Cheesecake Factory, The Melting Pot and dozens of other great places to eat... but you have to try Winsteads! It's an awesome burger place on the east side of the Plaza. Your DD would probably get a kick out of the Skyscraper Soda. A couple blocks away is the Nelson Atkins Museum of Art - it's also free and there are great photo ops by the giant Shuttle Cocks! (I have to admit, they've grown on me over the years).
There's the Harry S. Truman Museum, although I haven't done that in years, so I can't remember if it was good or not. We've also got a Zoo and I second the Steamboat Arabia and River Market
You'll get to see the Power and Light District - it's right across from the Sprint Center where the concert is. You can eat there if you want before hand, but I'd say get there early. We do have our own Raglan Road at P&L (same owner as in WDW) if you want that.
There is so much to do, I'm sure you'll have no problems filling your time! I

KC (can you tell?)
Have fun!
Rachel
p.s. I agree with the person who said World's of Fun is only ok, unless you like Roller Coasters; then it's pretty good!