Williams is an unincorporated town and census-designated place in Spice Valley Township, Lawrence County, Indiana, United States. As of the 2010 census, the population was 286. Williams is situated on the East Fork of the White River. Williams is home to Williams Dam, a hydroelectric dam that once powered the electricity for stone industries across souther…Williams is an unincorporated town and census-designated place in Spice Valley Township, Lawrence County, Indiana, United States. As of the 2010 census, the population was 286. Williams is situated on the East Fork of the White River. Williams is home to Williams Dam, a hydroelectric dam that once powered the electricity for stone industries across southern Indiana, especially in nearby Bedford and Bloomington.