+1 the National Music Museum. Not classical guitar-oriented, but just plain cool. They had Elvis Presley's Gibson and a Stradivari guitar at one point. USD incidentally offers one of the only advanced degrees in organology in the country.
I'll definitely vouch for the Museum of Fine Arts here in Boston. Lots of plucked strings, including a Frabicatore, a 9-string Lacote, and two Panormos (one of which is M. Sidney Pratten's "bambina" treble guitar).
Then stop by for a free NEC concert since you're down the block!
2015 Alan Chapman Test Friederich CD/CO
2009 Cervantes Concert Milenia SP/PE