Brooklyn is a city in Cuyahoga County, Ohio, United States. The population was 11,359 at the 2020 census. A suburb of Cleveland, it …Brooklyn is a city in Cuyahoga County, Ohio, United States. The population was 11,359 at the 2020 census. A suburb of Cleveland, it is a part of the Cleveland metropolitan area. Brooklyn was home to the first seat belt law in 1966 and the first cell phone law for motorists in 1999.