Elkwood, VirginiaElkwood is a town in Culpeper County, Virginia, United States. Elkwood is located on U.S. Route 15, east-northeast of Culpeper. Elkwood has a post office with ZIP code 22718.ClimateThe climate in this area is characterized by hot, humid summers and generally mild to cool winters. According to the Köppen Climate Classification system, Elkwood has a humid subtropical climate, abbreviated "Cfa" on climate maps.