Michael, there aren't many really decent hikes in central or western Missouri, especially the closer to KC you are. One area close to me (near Columbia, about two hours east of KC) is the Cedar Creek trail in the Cedar Creek District of Mark Twain National Forest. The easiest-to-reach trailhead is the Pine Ridge picnic/campground east of Ashland on Route Y. Ashland is about 15 miles south of I-70 on US 63, and the TH is about 8 or 9 miles east of Ashland. You can make any number of loops with country roads. The nicest section of the trail is accessible by taking the exit for Columbia Regional Airport (before you get to Ashland) and following that road east to its terminus at Rutherford bridge. Go through the settlement of Englewood and continue straight east. The road will eventually turn to gravel and ends at Rutherford bridge. Cross Cedar Creek there and follow the trail to some nice overlooks of the creek. You can camp along Smith Creek, a trib of Cedar Creek. It's all USFS.
Be aware, central Missouri in July can be miserable, with high temps, high humidity, numerous ticks, chiggers, and mozzies, as well as the occasional timber rattler. There will probably be water available, but it may be muddy and/or stagnant.
Southern Missouri, and especially SE Missouri has MUCH better prospects for hiking. There are numerous trails in USFS, state parks and conservation areas, including the Ozark Trail. It is not as easily accessible from KC, however.
PM me if you like, and I can help direct you to some trails, maps, Web sites, etc. jyancey(at)ktis(dot)com