Actually, according to William A. DeGregorio's useful factbook on the presidents, Coolidge's career before the Presidency included member of the Massachusetts General Court (i.e., state legislature), mayor of Northampton, Mass., Massachusetts state senator, Lieutenant Governor of Massachusetts, Governor of Massachusetts, and of course Vice President of the United States.
So he was never mayor of Boston, although it was the police strike in Boston in 1919 that brought him to national attention and led to his becoming the VP nominee in 1920.