In most every city in the United States the mayor is expected find his own place to live. It's our little nod to egalitarianism. There are a few exceptions.
New York City
Gracie Mansion is a 200 year-old rattrap on the East River. Okay, it probably doesn't have many rats but laws regulating the use of public property in New York means that neither Rudy Giuliani nor Michael Bloomberg could house their mistresses there.
The Getty House was given to the City of Los Angeles in 1975 so George Getty could take a tax deduction on one of his lesser homes. It's conveniently located just a couple miles from City Hall, meaning LA mayors hate it. The Hancock Park District wasn't ritzy enough for Dick Riordan while current mayor want to build a wall to keep his neighbors at bay.
Manoogian Mansion is located along the Detroit River in the finest neighborhood in Detroit. The worse thing I can say about the place is that Kwame Kilpatrick used to live there.
As nice as Detroit's mayoral mansion is, Denver's is over the top opulent. It has a multi-level swimming pool, a heated driveway, fire pole access to the master bedroom, and a pink grand piano. It was built by a cable TV magnate with no imagination (he called the place "Cableland") and donated to the city in 1998. No Denver mayor has been egocentric enough to sleep even one night there and the current mayor is desperately trying to sell the monstrosity.
At the other end of the spectrum, when Cory Booker was first sworn in a mayor of Newark in 2006 he continued living in a troubled public housing complex, not because he had to but because he choose to stay close to the people most needing attention.