While it may appear to be a state map within the Midwest US, the map of the train routes in the C & F.W. board room doesn't actually represent any real US states. No US states fit within the state borders represented on the map.
When a dinner guest asks why they built the Shady Rest hotel "way out in the middle of nowhere" (rather than in town), Kate explains that her grandfather was originally planning to build the hotel "down the track, in Pixley", but the flatcars carrying the lumber for the hotel tipped over when they hit the curve in the tracks, so her stubborn grandpa just went ahead and built the hotel right there.
On the wall map that Homer Bedloe (Charles Lane) and Norman Curtis (Roy Roberts) examine in the C & FW Railroad boardroom, some of the communities (or station names) in the vicinity of Hooterville Valley and its spur line from Hooterville to Pixley include Carlos, Delta, Melton, Pine Ridge, and Skidmore. It is not clear if the geographical boundary lines on the map represent division by county or by state.