The hamlet of Lakemont is located in the town of Starkey, New York which is in Yates County. It’s not far from the western edge of Seneca Lake, so this one can be found almost exactly in the center of the Finger Lakes Region.
According to some sources I’ve found online, the population of Lakemont is less than 6,000, which actually sounds really high after having spent some time there. This part of the state is super rural with lots of rolling hills and landscapes as far as you can see. Since their population is lower, I imagine they felt having a smaller Post Office would suffice.
I’m not sure that this is the smallest Post Office in the state, but it’s gotta be close!