Elkhorn City is a home rule-class city in Pike County, Kentucky, in the United States. The population was 1,035 at the 2020 census. The cit…Elkhorn City is a home rule-class city in Pike County, Kentucky, in the United States. The population was 1,035 at the 2020 census. The city is located in proximity to the Breaks Interstate Park. Elkhorn City was first settled by William Ramey of North Carolina c. 1810. However, in 1767–1768, Daniel Boone took his first steps in what is now Kentucky near present-day Elkhorn City on a hunting expedition.