As far as I understand, we can definitely say the phrase "the city of + name":
- when a city and a state have the same name, e.g.: "the city of New York" (or "New York City") and "the state of New York" (or "New York State").
- when "the city of + name" doesn't always mean the same as the name itself, e.g.: "the city of London" can mean not only the whole of London but (for some historical reasons) just the county in the very center of London.
Also there are the cities that don't have the properties described above but which (perhaps for some other reason) can still be called via the phrase "the city of + name". For example, Chicago on wikipedia.org is sometimes mentioned as "the city of Chicago".
So I'm interested to know:
Can we use the phrase "the city of + name" to any city in the world at all?
If not, then is there any rule about it?