Breckenridge is a city in northeast Caldwell County, Missouri, and is part of the Kansas City metropolitan area with the United States. The popula…Breckenridge is a city in northeast Caldwell County, Missouri, and is part of the Kansas City metropolitan area with the United States. The population was 258 at the 2020 census. Breckenridge was laid out in 1856, and named for Vice President John C. Breckinridge. A post office called Breckenridge has been in operation since 1860.