Eunice is a city in Lea County, New Mexico, United States. The population was 2,562 at the 2000 census. The mayor of Eunice, as of April 2007, is Matt White. Ground was broken for construction of a National Enrichment Facility to enrich uranium in August, 2006. An announced purpose is to make fuel for commercial nuclear power plants. Eunice apartments for rent comparison page shows most up to date rent information on Eunice apartments and houses. Rent information is obtained from multiple rental sources but we cannot guarantee their accuracy.