In Northern Missouri, near the Iowa and Illinois borders there is a farm where you pay the farmer a couple of bucks and he has hundreds of geodes on the property. Do a google search of the following: (( Missouri geodes)) and you will find where to go up there. Also go to this website:
Mineral Resources in Missouri
The above website lists minerals and locations. I don't think you will find any precious gems in the state if that is what you are after. Nearest location for those is "Crater of Diamonds" in Arkansas, but been there and it is hard work and lots of looking to find a diamond, but you may get lucky.