The Nelson-Atkins Art Museum is pretty amazing. Since it's free, I've been there more times than I can count. I'm pretty sure you won't be disappointed.
Those giant shuttlecocks are awesome. Mostly because they give you a reason to say the word "shuttlecock" preceded by any word you want meanings "big". You have to admit "shuttlecock" isn't a word you get to use in conversation very often, so it is always nice to have an excuse. The fact that they are very large in size just makes them all the more fun.
If you get a chance, I highly recommend talking someone over the age of 21 into going to a place called Grinders with you. It is a bar, but if you go during the day with an adult you should be fine, I've seen kids eat there before. Their Bengal Tiger Pizza is to die for (other pizzas are great too). Their chili, cheese, and tots are also pretty amazing if you feel the need to clog some arteries. It's at 417 E 18th St., not too far from the museum, actually. Mmmm, now I really miss it.