Potsdam is a town located in St. Lawrence County, New York, USA. The population was 15,957 at the 2000 census. The postal ZIP code is 13676. The town is named after the city of Potsdam in Germany. Potsdam apartments for rent comparison page shows most up to date rent information on Potsdam apartments and houses. Rent information is obtained from multiple rental sources but we cannot guarantee their accuracy.