Beekmantown is a town in Clinton County, New York, United States. The population was 5,545 at the 2010 census. The town name is that of William Beekman, an original landowner. It is on the easter…Beekmantown is a town in Clinton County, New York, United States. The population was 5,545 at the 2010 census. The town name is that of William Beekman, an original landowner. It is on the eastern border of the county, just north of Plattsburgh.