This series started in 2005 and is set in England. The books in this series do have the main character traveling to The Hamptons in New York. It features Lee Bartholomew who is a ghostwriter and solves crimes. She lives alone - by choice - in her parents' towering London house in Notting Hill.
The first two books in the series are available at Amazon and B&N, however the last 2 books are not available. I suggest checking at your local library or the authors' website.
Books in this series: