According to Christopher Bram, author of Eminent Outlaws: the Gay Writers Who Changed America, he moved to New York "to meet real gay men who might want to go to bed with [him] as eagerly as [he] wanted to go to bed with them." I think many would agree that those are fair motives to move to the Big Apple.
Bram told friends and family that he was moving for career opportunities as a writer, but he always thought that those were "lies" -- that he only ever wanted to move here for love and sex. While researching his new book, however, he realized that all of the above was true. He certainly wanted male affection, but he also wanted the companionship of other writers.
As it turned out, the same was true for the men he was researching. Tennessee Williams, James Baldwin, Truman Capote--they all moved to the city for writing and sex as well. For more, check out his blog post at MetroFocus.