Have Tom and Daisy Buchanan lived in East Egg very long in The Great Gatsby?
Yes, Daisy and Tom Buchanan do live in East Egg. They have lived there for a long time, as they are part of the established aristocracy. Those with money in their families, for generations as you have mentioned, generally live together. Here, on East Egg, properties are reserved for those with a history of wealth.
Those who have not had this same history of wealth, yet have come into a large sum of money in recent times, live and find life more comfortable in West Egg. This is a place for those with money, yet who are not part of the established aristocracy.
You are correct about people living for generations in East Egg. Generally, you must have had a property handed down, or else have had the money to buy such a property bequeathed to you by a well-to-do family member.
To answer this question, take a look at Chapter One. While Nick does not tell the reader exactly how long Tom and Daisy have lived in East Egg, there is a sense that they have not been there that long. Nick says, for example, that they were in Chicago just after the war. Then they spent a year in France before drifting "unrestfully wherever people played polo." In other words, Tom and Daisy moved around a lot, perhaps because they felt unable to find a place that they felt most comfortable and at home with.
Although they have not been in East Egg for long, Tom and Daisy intend on making it their permanent home. They have also purchased one of the grandest and most palatial homes in the area, which serves as an expression of their wealth and prosperity.