Turns out this is a more complicated question than I'd thought.
According to the Wikipedia main article on Washington (assuming you both mean the first President of the U.S. and not some other George Washington), he was at Mount Vernon when he was notified on April 5, 1789 that he had been elected President. He was inaugurated April 30, 1789 in New York City. Another Wikipedia article states he moved into the President's House in Philadelphia in November 1790.
So it's curious that he would have moved to Massachusetts.
Turns out that I do not have the resources to answer this question. I'm sure there are many biographies of Washington, and some WikiTreers may own some, but I do not. My old Encyclopedia Britannica was no help.