The NOAA data linked above gives highest average temperature as around July 22nd and the lowest average temperature as around January 17/18th.
So the midpoint between meteorological midsummer and meteorological midwinter in Boston is around October 20th. That would put the start of fall at around September 5th (give or take a few days as midsummer and midwinter aren't exactly six months apart so we can't really assume each season is 90 days long meteorologically).
US Labor Day or even September 1st seem much better dates for the "start of fall" than September 22nd.