There are 1 US Post Offices in Eureka County serving a total of 1,408 residents equating to 1,408 residents per post office. It's estimated that approximately 2,247 packages are handled across the 1 county post offices annually. Eureka County is a county located in the U.S. state of Nevada. As of the 2010 census, the population was 1,987, making it the second-least populous county in Nevada. Its county seat is Eureka. Eureka County is part of the Elko Micropolitan Statistical Area."