1. Big Apple
The Big Apple actually began as a way to refer to the horse-racing circuit of New York City. According to the Oxford English Dictionary (OED), it was used in the early 20th century to refer to 'something regarded as the most significant of its kind'. Soon, the term was being used with reference to the city itself. In 1970, the popularity of the term exploded, though, when it was part of a campaign led by Charles Gillett of the New York Convention and Visitors Bureau.
Broadway, which figures into the dreams of every high school theater buff, refers specifically to the cluster of theaters on or close to Broadway in midtown Manhattan near Times Square, but more allusively to show business at large. It's sometimes known as the 'Great White Way' due to the brilliant street illuminations and signage.
3. Empire City (and State)
References to the empire city and the empire state – referring to New York and New York City's prominent reputations – date back to the first half of the 19th century. In recent years, the term Empire State has seen some lift thanks in part to Jay-Z, whose song with Alicia Keys, 'Empire State of Mind', was a #1 Billboard hit in 2009.
4. Murderers' Row
New York City, it turns out, has played host to both a literal and a figurative murderers' row. The first instance of murderers' row refers to the row of cells in a prison, originally in NYC's Tombs Prison, in which condemned murderers or other violent criminals are held. The figurative use of murderers' row comes from baseball slang, meaning a 'group of powerful hitters batting in succession for a particular team', notably the New York Yankees of the 1920s, which included Babe Ruth and Lou Gehrig.