The two crossword solutions for the term 'New York City Nickname' are 'Gotham' (6 letters) and 'Big Apple' (8 letters). Both of these nicknames have been used to refer to New York City since the late 19th century. 'Gotham' is a reference to the fictional city in which Batman lives, which was inspired by New York City. 'Big Apple' is a reference to the city's reputation as a major center of culture and commerce.