This file from NOAA looks like it has the necessary data for Boston. I haven't parsed it yet to do a "windowing" based calculation of peak date but given it's averaged over 30 years (I assume from the URL) it's pretty smooth.
Visually inspecting it, it appears the peak average temperature is around July 22nd, a full month after the solstice. That would put the meteorological start of summer in Boston around June 7th.