Perhaps no mythical beast associated with a city, at least in the western canon, is more famous than the Lupa at the center of Rome's foundational myth.
The legend puts the abandoned infant twins Romulus and Remus at the Tiber, that carries them to to the base of the Palatine Hill where they are suckled and cared for by a she-wolf. The story is well known: the twins grow up as shepherds, learn about their divine origin and decide to found a city along the river. Romulus chooses the Palatine Hill, Remus the Aventine Hill, they fight, Remus is killed and Romulus founds Rome, naming the new city after himself (modern historians, of course, put the relation between the names the other way around.)
The she-wolf with the infant twins became an emblematic figure inextricably linked to Rome. One of the best known representations of the legend, the Lupa Capitolina has a story of its own. The figures of Romulus and Remus were added to the sculpture of the wolf in the Renaissance. As for the wolf, it was thought to be of Etruscan origin, dating back to the 5th century BC, but turned out to be a Medieval casting.
By the way, when you look at the topography of the area, don't you think that Romulus choice--the Palatine, smack at the center of Rome's seven hills--was a much better place for the foundation of the city?