Is Milwaukee city a common noun?

No, "Milwaukee city" is not a common noun. It is a proper noun.

A common noun is a name for a general category of things, such as "animal" or "book". A proper noun is a name for a specific person, place, or thing, such as "George Washington" or "Mount Everest".

"Milwaukee" is the name of a specific city, so it is a proper noun. "City" is a common noun, because it refers to a general category of places.

When we write a proper noun, we capitalize the first letter. So we write "Milwaukee city", not "milwaukee city".