What does nick learn by the end of the novel, and why does he ultimately return to the west?

Nick has come to realize that he’s changed and will never be the same. It seems his character dilemma is never fully resolved. We do not know where he will go ("West" is pretty vague), or what he will do, only that he is leaving the house he's resided in for the course of the book. His observation that all the players in this story were “Westerners” is an apt one – it sums up one of the novel’s main themes, the idea that we might be defined by where we’re from, or the kinds of worlds we grow up in.

Nick ultimately realizes that he has no place in West Egg or in New York, in the callous, judgmental, and fast-moving East; unfortunately, we have to wonder if he can really go back home again, after seeing what he has seen. Though he used to believe that you couldn’t turn back the clock and return to the past, Nick’s perspective has changed: his neighbor Gatsby is gone. Tom and Daisy are gone. Jordan Baker is gone. Nick's greatest fear – that he will be alone – has come true.

The final lines of the text suggest the inevitability of what will overcome Nick: inclinations towards Gatsby's nostalgia and an inability to separate the dreams of the past with the reality of the present. And if you want further evidence for that one, consider the fact that Nick is telling us this story at all, after it has all unfolded – he's still dwelling in the past.