Multiple realities(covers information from several alternate timelines)
On Earth, a mayor was the head of government of a city, town, or village. It was similar to the title of tetrarch, used on the planet Bajor. (DS9: "The Storyteller")
In an alternate timeline February 1936, the mayor of New York City approved a budget increase. The story was reported on by The Star Dispatch, who noted that the city council was debating the budget changes. (TOS: "The City on the Edge of Forever")
In reality, the mayor at that time was Fiorello La Guardia, after whom the airport is named.
Reuben Lara was the mayor of Los Angeles in the 1990s. (VOY: "Future's End")
The Honorable Helen Burke served as mayor of the of San Francisco during the Bell Riots of 2024. (DS9: "Past Tense, Part II")
In 2365, Doctor Katherine Pulaski jokingly asked Kyle Riker if he was running for mayor. (TNG: "The Icarus Factor")
According to Marie Picard, for the return of Jean-Luc Picard to La Barre France in 2367, the first time in twenty years, the village's mayor wanted to give Jean-Luc a parade, but was told not to make plans without talking to the Picards first. (TNG: "Family")