While working on an unrelated post, I was reminded of the historical USGS topographic maps that have been posted online.
The image on this post comes from the 1933 map for Carthage, Hancock County, Illinois. The only modification I made to the map was the "Fred & Tena Ufkes farm" notation (and the black line pointing to their house). My great-grandparents, the Ufkeses, would have been living there in 1933. All the Ufkes children (including my grandfather) attended the Union School which is shown in the northwestern corner of section 24 of Bear Creek Township. Not too far of a walk and a fairly flat one from the map (which I already knew).
These historical maps on the http://historicalmaps.arcgis.com/usgs/ site are a wonderful resource and a great way to locate former one-room schools. Churches are also indicated. There's one to the very very small "+" to the right of "farm." Cemeteries may also be noted as well, sometimes unnamed. There cemetery affiliated with the church near the Ufkes farm is approximately one mile north of the church and is indicated with an + with a box around it.