Callaway is a city in Bay County, Florida, United States, and is a suburb of Panama City. The population was 13,045 at the 2020 census, down f…Callaway is a city in Bay County, Florida, United States, and is a suburb of Panama City. The population was 13,045 at the 2020 census, down from 14,405 at the 2010 census. It is part of the Panama City–Panama City Beach, Florida Metropolitan Statistical Area.