In Chapter 1 of The Great Gatsby, why is Nick back from New York?
Concerning The Great Gatsby, I'm not sure what you mean by "back from New York." Nick is originally from the Midwest, works in New York, and is currently living on that "slender riotous island which extends itself due east of New York..." and amounts to "a pair of enormous eggs, identical in contour and separated only by a courtesy bay,..." Nick lives at West Egg, and most of the story takes place there and on East Egg.
Nick is on the East coast to work, and he took the house he took because of its proximity to the ocean and the ocean view, its view of the neighbor's lawn, and because it is surrounded by millionaires, all for eighty dollars a month.
Your question is slightly ambiguous, but here are several interpretations of it. Nick works in the city and lives on West Egg near Gatsby's mansion (which is a setting slightly outside of New York City). So, in a sense, in Chapter 1 when he is going over to Tom and Daisy's, he's "back" from New York because he's done with work for the day/weekend.
If you are actually referring to why Nick left his hometown of Chicago, he explains in Chapter 1 that he came East for a job but also for a new experience. This move on Nick's part is key to Fitzgerald's theme of the East "corrupting" Midwestern values and morals.