Peter is considered "the Father of Oyster Bay".
Shortly after their marriage, Peter and Alice settled in Lynn, Essex Co, MA where their first child, Job, was b. in 1636. They migrated to Long Island apparently to get away from the Puritan hegemony.
The General Dictionary of First Settlers of New England, Savage, Vol. IV, pp 638, and the Plymouth Records, Vol III, pp 11, both say that Peter and his family became members of The Society of Friends (Quakers) after they settled in Long Island in 1653, where he bought Oyster Bay from the Indians.
Alice was an active and prominent member of the Oyster Bay community. Three of Peter's daughters, Mary, Hannah and Lydia, were Quaker activists, and all three individually made trips to New England to protest the treatment of Quakers (and were severely hounded as a consequence). Hannah died unmarried, but Mary married Samuel Andreas and Lydia married Isaac Horner. Both moved with their families to Burlington County, New Jersey, to escape the persecution.
For a detailed history of their travails, visit: http://www.lihistory.com/3/hs345a.htm.1
From Alice (Wright) Crab's will:
In the name of God, Amen. I, ALICE CRAB, of Oyster Bay, I leave to my daughter Lydia Horner, the shares of meadow, adjoining the meadow once of Nicholas Simkins, in the Town meadow. And two shares by the will of my brother-in-law Anthony Wright. I leave to my daughter Mary Andrews, and my grandchild Job Townsend, all my land and meadow at the South, and at the Plains, all which did belong to my brother Anthony Wright. I leave to my granddaughter Alice Townsend, one little iron pot and pewter plate. My negro man is to be free, but he is to pay €4 to Simon Cooper and James Townsend for the use of my grandson Job Townsend. I leave to my three sons, Gideon Wright, Jacob Wright, and Adam Wright 5 shillings each. I make my two sons-in-law, Samuel Andrews and Isaac Horner, executors.