There was a Thomas Whittemore (1755-1829) from Leicester, Massachusetts who moved to New York City. He married (1) Lucy Snow and (2) Hannah Sheldon and had 12 children. Apparently the Whitmore, Whittemore, and Wetmore families in New England are all related, and descended from a Whittemore ancestor. The article, "The Whittemore Family in America" was published in the New England register, 1952-1954.
There were many Dutch settlers in New Jersey and along the Hudson River in New York, especially in areas like Albany and Rensselaer, NY; Orange Co., NY, Monmouth Co., NJ, and neighboring counties. You might check the Reformed Dutch Church records.