Warrensville Heights is a city in Cuyahoga County, Ohio, United States. It is an eastern suburb of Cleveland. The population was 13,789 at the …Warrensville Heights is a city in Cuyahoga County, Ohio, United States. It is an eastern suburb of Cleveland. The population was 13,789 at the 2020 census. Warrensville Heights is located at 41°26′19″N 81°31′24″W / 41.43861°N 81.52333°W.