Honestly, if you are touring the US... just do what everyone else does and skip our state. Nebraska/oklahoma too. But maybe that is just because i have lived here all my life.
If you come, definitely hit up some BBQ in KC. And Do some driving through the flint hills area.
visit Kansas Rocks on an event weekend, tons of cool offroad vehicles, food, events to watch, timed crawling competiton on the rock garden, and tons more
As others have said, there are some good places to go 4-wheeling. Kansas Rocks is a great place for rock crawling and trail riding, and Tuttle Creek has a great area at in the state park. As I see you have a Jeep I recommend both!