First thing to do is get online to the MO website at :
http://mdc.mo.gov/ Then under quicklinks on the left side, click on "Conservation Areas". This will bring up their Atlas and you can search by area name, county or region and get info on state areas in the area you are interested in.
I'm guessing though that what you are really looking for is first hand references to areas known to be good for deer. I'm not the best guy to talk to about that. I don't like to drive far to hunt so I pretty much just hunt the areas closest to me and I'm over by the north side of Kansas City so I'm limited. If you are interested in hearing about areas over here, I'd be willing to help ya out.
Also, look on the website and see if you can find the printed copy of the Conservation Atlas. It's a big ol' spiral bound atlas that runs county by county and shows all the state land. The best thing about it is that it shows all the little back roads that are often left off on regular maps and they also have a chart for each area that rates the population/quality of hunting for each common species. i.e. say deer, will be rated as poor, fair, common, abundant or something like that.
A little tip, many areas owned by the state were purchased for a specific reason like some sort of geological or ecological feature that is unique. Might be marsh/swamp and the area could be managed for ducks or it might be for some sort of limestone spring, a stretch of unchannelized river, old growth forest of some sort or even grassland. On the site, it usually mentions these and take them into consideration. Areas managed for duck hunting are often some of the best in the state for deer hunting due I think to the fact that big bucks have webbed feet... Well, you know what I mean. Ducks and deer just go together.
Lastly, don't forget to check on federal land and corps of engineer land. Any corps lake will have public hunting around the perimeter out to the high water mark and in many places it's thousands of acres. Of course, a boat is the best access to those places but they do have public access points on all of them. It's just that you can do a lot of hoofing it around various arms of a lake to get to the spot you want to hunt if you don't have a boat and the boat also makes for a lot easier "drag".
Good luck!