For sure try browsing the MDC web page.
http://mdc.mo.gov/ If you will be driving around in your own vehicle, I'd also suggest buying a "Missouri Atlas and Gazetteer" and the "Missouri Conservation Atlas" as both show nearly all the little dink roads in the back country and also show the public lands. The conservation atlas is the better of the two as it has tables in the back that break down each conservation area by activities available, species available and how abundant they are along with other info from the MDC.
You can get full access to the MDC atlas online by clicking on [Conservation Areas] in the left menu on the site I linked above. You can then enter a known area name, a county or a region and get a list of MDC public lands. For example, I live in Platte County. If I use the drop down menu on the county block I can find Platte and enter it. That gives me a list of 11 public land areas in my county. Platte Falls CA is where I usually hunt so if I click that, it pulls up this:
http://mdc4.mdc.mo.gov/applications/moatlas/AreaSummaryPage.aspx?txtAreaID=7929&txtAreaNm=&txtCounty=PLATTE&txtRegion=&txtUserID=guest&txtDivision= The left menu allows you to see all sorts of information. The [Area Map] will give you an exact copy of the map on the fliers available in the parking lots of the area. The parking lots are the little black squares.
The [Area Regulations] block will give a complete rundown of seasons, bag limits, restrictions etc.
If you have an area, county, region etc in mind, you can get a ton of info this way. Best of luck to ya.