New Washington, OH. Sponsored Topics. New Washington is a village in Cranberry Township in Crawford County, Ohio, United States. The population was 987 at the 2000 census. New Washington is located at 40°57′41″N 82°51′20″W / 40.96139°N 82.85556°W / 40.96139; -82.85556 (40.961465, -82.855446).