For what do New York City, the valley of ashes, West Egg and East Egg stand in The Great Gatsby? In which way are they different from each other?
Each of these locations means something slighty different to Gatsby, Daisy, Nick, Tom, etc., but there are some commonalities. New York is for Tom a place to play and misbehave with his mistress Myrtle. For Myrtle, New York is escape from her horrible life with her husband (in the "valley of ashes"). New York for Nick is a place of a different kind of opportunity -- success in business. It is, for most characters, an "other" place. A place outside of most of the action of the story, it is a place that's an escape from the oppressive atmosphere of Long Island. The "valley of ashes" represents the real world of most of the people of the United States. It is a blighted, poor area in which Myrtle and her husband live. It is ugly and depressing, and is in contrast to the bright lights of the city and the protected beauty of West and East Egg. It is quite literally a place of death (Myrtle's), rather than one of life or hope. West and East Egg represent where the best of society should be at peace. Tom and Daisy are in the very best section (East Egg), while the parvenu Gatsby and the relatively poor Nick are left to gaze with longing across the water at East Egg from the less-fashionable West Egg. East Egg represents, at least for Gatsby, a kind of unattainable heaven (containing Daisy). West Egg was supposed to be a refuge from the city's heat for Nick, but as the events of the summer unfold it becomes a place of sadness and lost hopes.
West Egg symbolizes "new money," the people who have had to work, or otherwise earn their fortunes, rather than inherit them. West Egg is where these people, who want to fit in with the "old money" folks from East Egg, live, because all of the homes and estates in East Egg are passed down from one generation to the next and cannot really be purchased. This is why Gatsby has to settle for West Egg (when he would really rather live nearer to Daisy in East Egg). The homes in West Egg, homes like Gatsby's, seem a little gauche, over the top, new to the kind of understated elegance that characterizes the people in East Egg.
East Egg is where the very rich people who have inherited their fortunes live. They don't have to try hard to prove that they are wealthy and classy, because they possess the self-assuredness of someone who's never had to work for their money. The Valley of Ashes represents the detritus of society: the people, the garbage, the ashes. We associate ashes with death, with something burned up, with whatever's left once something's been used. The people who are used up by industry, who have to work their entire lives but will never have one tenth what those people in the Eggs have, who are exploited by the newly-rich in West Egg in factories and big business: these are the people who live in the valley of ashes. And New York City is the place where all of these groups come together.