Everyone knows that the phrase The Big Apple is a name for New York. There is some doubt about where it comes from but most experts think it is related to a slang term for a racecourse. You can find a full discussion of this on Wikipedia: http://en.wikipedia.org/wiki/Big_Apple.
In Daniel Cassidy’s crazy book How The Irish Invented Slang, Cassidy claims that NY is sometimes known as The Big Onion, though others disagree and say that this refers to Chicago. Cassidy claims that this is not a jocular reference based on The Big Apple, which is the assumption any sensible person would make in the absence of good evidence to the contrary. He claims it comes from the Irish word anonn and that it means ‘The Great Beyond’. Irish maintains a distinction between words which relate to movement and words used of static situations. Thus you go amach (out) but you are then amuigh (outside). Similarly, anonn is a word used of movement to the other side. The other side or the beyond is thall in Irish so this claim is ridiculous both from the perspective of English and from the perspective of Irish.