Avignon, France, is sometimes referred to as the "City of Popes" because of the presence of popes and anti-popes from 1309 to 1423 during the Catholic schism.
There have been 13 popes called Leo, and there appears to be no dispute about the numbering, as is the case with a few of the popes. See links.
the popes live in the papal apartments in the apostic palace in vatican city
There have been 8 popes called Urban.
There have been 13 popes named Innocent.
Yes, they had many differences on matters of authority and doctrine. Some Popes were even excommunicated by Church Synods (or Councils) and other rival Popes were elected in their place, called Ante-Popes.
Vatican City, an independent city state, is located entirely within the city of Rome, Italy.
There have been 6 popes who chose the name of Paul.
Popes & Patriarchs.
Avignon was official home of the Popes. I've been there. That is a likely choice.
There have been 15 popes named Benedict. Pope Benedict X does not count as he was an antipope.
Avignon, France