Amherst is a town in Erie County, New York, United States. Amherst is an inner ring suburb of Buffalo. As of 2010, the town had a total population of 129,595. This represents an increase of 5.9% from th…Amherst is a town in Erie County, New York, United States. Amherst is an inner ring suburb of Buffalo. As of 2010, the town had a total population of 129,595. This represents an increase of 5.9% from the 2010 census.