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 be explicit with grammar references.