Capitals for a city nickname?
Solution 1:
A word or group of words {such as “Noah Webster,” “Kentucky,” or “U.S. Congress”} that is the name of a particular person, place, or thing and that usually begins with a capital letter
is a proper noun. --Merriam-Webster Dictionary.
That would include nicknames.
Articles preceding such are not capitalized unless they begin a sentence, following the Chicago Manual of Style, 16th Edition:
the Eternal City
the Windy City
If an expression is used merely to describe a city, they would not generally be capitalized in prose or under "sentence style".