In Chapter One, we see where Nick came from and why he has gone East. We learn that his family started poor and worked themselves into a strong family in his town, that Nick went to a premier school, that he fought in the war, and that he is currently studying bonds. He fits into West Egg, the less fashionable Egg, because he is new to town, and his families' money in relatively "new" money. He isn't wealthy as Gatsby is wealthy, but his family has worked hard for the money they have. Nick has worked hard to get to his current position. The idea of "new" money is associated with West Egg.
At the same time, he is related to Daisy and he went to school with Tom and Daisy both. This puts him in society with the East Egg residents, those whose money is a deep-rooted family tradition. Nick is there to study bonds, he isn't currently in school or employed, so he is able to enjoy the leisure of life that the East Egg residents enjoy too. In these ways, he fits into both societies.