After reading the following dictionaries entries:
I've realized that "ville" is an agglomeration of people and buildings, which can be translated to English as "city" or "town", depending on the context. On the other hand, "cité" usually refers to a poor suburban area with homogeneous architectural style ("ghetto" or the US euphemism "project" in English). Other less usual meanings are "historical center" of a city and "city-state", a term commonly used to refer to some ancient independent cities such as Athenas and Rome in olden times.
What is confusing to me is that it seems that "cité" can also be used as a synonym of "ville". Ex: La cité de Paris n'est pas très étendue. I have never heard the word "cité" with such meaning in the news or in TV movies/series which take place nowadays, so I think this meaning is rarely used these days?