Brunswick is the largest city in Medina County, Ohio, United States, approximately 20 miles southwest of Cleveland. The population was …Brunswick is the largest city in Medina County, Ohio, United States, approximately 20 miles southwest of Cleveland. The population was 35,426 at the 2020 census. It is part of the Greater Cleveland. Brunswick was founded on January 1, 1815, and was named randomly in a naming contest after Brunswick, Germany. It was incorporated as a village on February 1, 1960, and incorporated as a city on October 2, 1960.