The family genealogy book, by Thos J. Twining of Sydney, Indiana (Published 1890), titled "Genealogy of the Twining Family Descendants of William Twining Sr. Who Came from Wales, or England, and died at Eastham, Massachusetts 1659. With information of other Twinings in Great Britain and America."
is available for viewing and research at
From page 10: "Mr. William Twining, who first appears in public records, as a freeholder at Yarmouth, on Cape Cod, Massachusetts, in the year 1643,though there is reason to believe that he came over at a somewhat earlier date. "
The book contains an Index of the heads of family that may be of interest, even if you have no interest in the Twinings.