There are several definitions of the word city. In my mind a city is where a large number of people live. Sometimes cities are not that large they are called cities because that is what their founders named them, for example I know of a city that has less than a thousand citizens but is still called a city.
From where I live the closest city with a large population that is good for shopping and recreation is Las Vegas Nevada. At the same time for people that live in smaller communities may consider the city I live in “The City”.
To some people the only real city in the United States is New York City. Many years ago I visited New York City and I’m glad I did. I would even like to visit the city again but I wouldn’t want to live there.