>>2367953KC is /out/ purgatory. Anything really good is at least a four hour drive. Look up the National Forest outside Columbia though, that's only two and a half hours away and it has a couple quaint trails. If you're up to the drive, look into Bell Mountain Wilderness in the east and Hercules-Glades Wilderness in the southwest. The former has the most dramatic views in the state, the latter has the most varied land tract. You'll have fun backpacking either.
On the Kansas side, you'll want to grab a State Park vehicle pass and check out Kanopolis State Park in the spring or fall. Neat area with some cool trails. There are other parks I'm going to explore that look decent, but as you know Kansas doesn't have much in the way of public land. One cool thing about the state is their annual camping pass, which you can get for $200-$250. It's unlimited non-utility camping in any state park year-round. Only one other state in the country offers an annual camping pass, New Mexico.
Any questions about the area, feel free to ask.