The absolute best place to find information about East Egg and West Egg is in the very first chapter of The Great Gatsby where the narrator (Nick Carraway) describes both places in great detail. First, Nick gives the geographic location of East Egg and West Egg which are both located on Long Island, New York. "It was on that slender riotous island which extends itself due east of New York—and where there are, among other natural curiosities, two unusual formations of land" (4). Next, Nick speaks of the East Egg and West Egg in regards to their similarities and differences:
Twenty miles from the city a pair of enormous eggs, identical in contour and separated only by a courtesy bay, jut out onto the most domesticate body of salt water in the Western hemisphere, the great wet barnyard of Long Island Sound. They are not perfect ovals--like the egg in the Columbus story, they are both crushed and flat at the contact end--but their physical resemblance must be a source of perpetual confusion to the gulls that fly overhead. To the wingless a more arresting phenomenon is their dissimilarity in every particular except shape and size (5).
Nick then describes, in detail, the specific differences between the two. Nick deals with West Egg first because that is where he lives. "I lived at West Egg, the--well, the less fashionable of the two, though this is a most superficial tag to express the bizarre and not a little sinister contrast between them" (5). Then he deals with the area that perplexes him the most: East Egg. "Across the courtesy bay the white palaces of fashionable East Egg glittered along the water, and the history of the summer really begins on the evening I drove over there to have dinner with the Tom Buchanans" (5).
In other words, the filthy rich live in the two Eggs. However, there is a big difference between them: East Egg holds the "old rich" who have always known money while West Egg holds the "new rich" who have only recently acquired wealth. East Egg and West Egg are nicely foiled by the Valley of the Ashes, which is described succinctly in the second chapter.