Princeton is the county seat and largest city of Mercer County, Missouri, United States. The population was 1,007 at the 2020 census, down fr…Princeton is the county seat and largest city of Mercer County, Missouri, United States. The population was 1,007 at the 2020 census, down from the 2010 census, which counted 1,166 people. Princeton was the birthplace of the famous frontierswoman Calamity Jane.