Well, there is an interesting paper on Stuyvesant by a scholarly descendant at this site, which includes this bit:

In the spring of 1651 Stuyvesant purchased from the Dutch West India Company land which he called the Great Bowery (or farm). This property ran from the East River to the present Fourth Avenue and Broadway in an area bounded by Fifth Street on the south and Seventeenth Street on the north, roughly the Lower East Side of Manhattan. He paid 6400 guilders for the land. He had a house there, a barn, six cows, two horses and two young Negroes. It was clear that Stuyvesant meant to remain on Manhattan for some time.