‘City’ is a common noun. Common nouns are general names for a person, place, thing, or idea, and they do not refer to something specific. In contrast, a proper noun names a specific person, place, or organization and is always capitalized.
For example, ‘city’ can refer to any urban area, like a town or metropolis, without indicating which one. However, if we say ‘New York City’ or ‘Los Angeles,’ we’re referring to specific places, which makes them proper nouns.
So, while ‘city’ itself is a common noun, specific city names are proper nouns.