Exeter is a town in Washington County, Rhode Island, United States. Exeter extends east from the Connecticut border to the town of North Kingstown. It is bordered to the north by West Greenwich and East Greenwich, and to the south by Hopkinton, Richmond, and South Kingstown. Exeter's postal code is 02822, although small parts of the town have the mailing address West Kingston or Saunderstown. The population was 6,425 at the 2010 census.Exeter was named for the Earl of Exeter.