Andover is a town in Merrimack County, New Hampshire, United States. The population was 2,406 at the 2020 census. Andover includes the villages of Cilleyville, Potter Place, East Andover, and West Andover, in addition to the town center. The town is home to Ragged Mountain State Forest and Proctor Academy, a private coeducational preparatory sc…Andover is a town in Merrimack County, New Hampshire, United States. The population was 2,406 at the 2020 census. Andover includes the villages of Cilleyville, Potter Place, East Andover, and West Andover, in addition to the town center. The town is home to Ragged Mountain State Forest and Proctor Academy, a private coeducational preparatory school.