In Florence instrument shops are mainly mainstream. The largest is Ceccherini - via dei Ginori (actually, it is housed in the Ginori palace and belongs to the Ginori family). Smaller shops are:
Checcacci - corso dei Tintori
Saporetti e Cappelli - via dei Conti
Onerati, on via Il Prato, is a very good shop for wind instruments, probably the best selection in central Italy and a good workshop.
Play! drum and Percussion, via Monteverdi: I should check if the shop is still open. Several years ago was among the best shops in Italy for percussions, but they went broke and later reopened with this new name. Since then, I did not hear about them again.
There are several violin makers shops, but I guess the original poster probably will not be interested. In Sesto Fiorentino, few meters from the train station, there is a large store for electronic music equipment (an even larger one should be in Siena, but it is a lot of time I do not visit them).
Pistoia is an important center for cymbals and metal percussion instruments. The main maker is UFIP
Luca Logi aka itarchivarius