There are 6 US Post Offices in Grayson County serving a total of 11,546 residents equating to 1,924 residents per post office. It's estimated that approximately 18,429 packages are handled across the 6 county post offices annually. Grayson County is a county located in the southwestern part of the Commonwealth of Virginia. As of the 2010 census, the population was 15,533. Its county seat is Independence. Mount Rogers, the state's highest peak at 5,729 feet (1,746 m), is in Grayson County."