We lived there in the past and it's a hidden gem. You should absolutely see the WWI museum! It is much smaller than the WWII museum in New Orleans but still very significant. Union Station next door can have major traveling exhibits that are very interesting, you just need to check the website and see what's in town. The American Jazz Museum is also excellent. The Truman Library in Independence is absolutely worth a visit. Since it is older it is much smaller than other presidential libraries. He is buried there as well. There are fantastic shows at the Kansas City Symphony and the Kauffman Center for performing arts has numerous programs throughout the year. The T-Mobile Center also has lots of special programs and the Power and Light District across the street is a fun place to outdoor concerts/festivals/bars, etc. Nelson-Atkins Art museum can get major traveling shows as well and the Country Club Plaza is a "main-street mall" if you like shopping. Westport is a cool area for vintage shopping and we like Morningside/Brookside for restaurants. City Market on Sunday morning is a sight and there are many ethnic restaurants in the vicinity and the Arabia Steamboat Museum is very unique if you like historical artifacts.
We absolutely LOVED living there and have been back many times over the year to visit friends and it's always fun! KC has all the great stuff of most major cities with farmer pricing and very little traffic, so you can enjoy more things.
Jack Stack BBQ at the freight house is our favorite but we also like Grunauer next door.