Do Not Capitalize
Such words as city, state, county and village are capitalized only when they refer to the actual government.
Do you capitalize city of Chicago?
Capitalize city only when it is part of the city's name (New York City, Kansas City, Sun City), its creative name (Windy City for Chicago), or the name of the governmental body.
Do you capitalize Baltimore city?
BALTIMORE, BALTIMORE CITY
When Baltimore City must be used to refer to the city government, City should be capitalized.