“There was another settlement too Jamestown, which would have preceded Plymouth, but it did not survive.”
You need a new history book. Jamestown certainly did survive.
The Roanoke Colony of 1587 vanished, not Jamestown.
According to this, Saint Augustine, Florida is the oldest continuously inhabited European established settlement in the United States – 1565.
St. Johns Newfoundland is the oldest English-founded city in North America – 1583
Jamestown Virginia was the oldest colony in the original thirteen colonies comprising the United States of America – 1607. And Jamestown served as the capital of the colony for 83 years, from 1616 until 1699. However in 1699, the capital was relocated from Jamestown to what is today Williamsburg, after which Jamestown ceased to exist as a settlement, existing today only as an archaeological site. So yes, Jamestown did survive as a settlement for 83 years.
Hampton Virginia (1610), Newport News Virginia (1613) and Albany New York (1614) all predate Plymouth (1620).