Four distinct geographical areas are important in The Great Gatsby: West Egg, East Egg, the Valley of Ashes and New York City. What are some ways...

This is a great question, and very interesting to explore. This topic lends itself to a multi-page essay, which I'm not going to write here, but I can give you an overview which you can develop.

First, we have to take a close look at each of the four zones and which characters/values they are associated with:

West Egg is where Gatsby lives. It symbolizes new money. Gatsby started out a poor farm boy and created his own wealth. West Egg is the site of extravagance, as shown by Gatsby's wild parties.

East Egg is where the Buchanans live. It represents old money, or the established aristocracy, people like Tom who come from wealthy families, don't have to work for a living, and enjoy a high social status. This East Egg upper class enjoy an extravagant lifestyle as well, but their activities are more subdued than in the West Egg. Tom keeps horses and plays polo, and Daisy enjoys leisurely afternoons with her friends. The aristocracy look down on the new money.

The Valley of Ashes is where the Wilsons live. They came from nothing and are going nowhere. The ashes symbolize their desolation and hopelessness. George works hard every day at a labour-intense job just to maintain a small, dingy home. Both West Egg and East Egg folk regard the Valley of Ashes as merely a passageway to New York City.

New York City is a busy, chaotic metropolis. None of the main characters live there, but they do go there for various activities, giving the reader the sense of the corruption and carelessness that Nick finds in the East, ultimately prompting his return to his home in the American Midwest.

Now we need to look at what events take place in each of these zones that lead to conflict:

West Egg, as mentioned, is the location of Gatsby's extravagant parties. A conflict arises when Tom Buchanan and his friends stop off at Gatsby's on a horse ride and show thinly-veiled contempt for Gatsby, and another when Tom attends one of Gatsby's parties and again shows his arrogance and distaste for Gatsby and all that he symbolizes (new money).

In East Egg, at Tom's house to be specific, we have a major conflict when Gatsby attends a dinner there. He reveals his desire for Daisy in front of Tom while Tom is busy setting up plans with his mistress, Myrtle. All this cheating, or lack of family value, creates anger which encourages the party to go into town (New York City). This sets up the final confrontation between Gatsby and Tom, and the climax—Gatsby's car hitting and killing Myrtle.

The third setting, the Valley of Ashes, is where Myrtle dies and Tom is forced to confront his own values via his love for his mistress vs. his comfortable and appropriate marriage to Daisy. Gatsby also confronts his own values here via his love for Daisy, when he chooses not to reveal that it was her who was driving the car when it killed Myrtle.

Finally, New York City is the site where Nick becomes privy to Tom and Myrtle's love affair in the apartment Tom has rented for them, and has to confront the value of loyalty to family (Daisy) vs. loyalty to friends (Tom). It is also where Nick meets Meyer Wolfsheim and has to confront his values regarding legal vs. illegal money when he realizes that Gatsby keeps some rough company. Finally, the conflict between Tom and Gatsby over Daisy takes place here when Gatsby tries to make Daisy say she never loved Tom.

These are just some examples and will need further explanation and evidence from the novel to support them. You might be able to find some appropriate quotes  I hope this helps. Good luck with your essay!