Dillons Run, West Virginia  Dillons Run was an unincorporated community in Hampshire County, West Virginia, United States. It is located at the intersection of Dillons Run Road (West Virginia Secondary Route 50/25) and Haines Road along Dillons Run stream from which it takes its name. Dillons Run no longer has its own post office  in operation. It was originally known as Luptons Mill.