Say we pick a city, NotLondon. Now assign a nickname, "NotLondon, the city of tears", tears being a metaphor for rain. Should these be capitalized? Should the word 'the' be capitalized? I think it counts as a proper noun, in which case the answer would be yes.
New York: the Big Apple seems obvious to me (although it seems 'the' is not part of the nick name as it is not capitalized), but when using words to describe a city rather than naming it (the city of tears), I'm not so sure. The description is its nickname.
English is not my native tongue, so please explicit with grammar references.