do they have a holy city?
Yes, Vatican City
Catholic Church
The pope is also Sovereign of Vatican City, a small city-state entirely enclaved within the city of Rome, which is an entity distinct from the Holy See. 
what was the structure of the roman catholic church based on UNANSWERABLE who is the head of this church? Pope
wiki:13008059
Catholic Church [SEP] Holy See, papacy, Roman Curia, and College of Cardinals
The pope is also Sovereign of Vatican City, a small city-state entirely enclaved within the city of Rome, which is an entity distinct from the Holy See. It is as head of the Holy See, not as head of Vatican City State, that the pope receives ambassadors of states and sends them his own diplomatic representatives. The Holy See also confers orders, decorations and medals, such as the orders of chivalry originating from the Middle Ages. While the famous Saint Peter's Basilica is located in Vatican City, above the traditional site of Saint Peter's tomb, the papal cathedral for the Diocese of Rome is the Archbasilica of Saint John Lateran, located within the city of Rome, though enjoying extraterritorial privileges accredited to the Holy See.