The area around via Maso da Finiguerra, via Palazzuolo and surrounding streets is known for a bit of urban decay, vagrancy, drug related activity, and micro criminality (shop and car break-ins particularly). It’s always been that way a bit (the Business School of the University of Florence I attended was nearby), but now is a bit worse with the arrivals of many unhoused migrants who tend to hang out in that area. During the day the area is perfectly ok, but after dark less so. Nobody will mug you at a gunpoint, but you may be bothered by panhandlers, drug dealing activity by some pushers, and a woman walking alone might be targeted for unpleasant behavior, occasionally there have been instances of theft and purse snatching of tourists or seniors, but rarely (and those can happen everywhere). The main complaint is the “spaccate” (shop window smash and grab).
Now I don’t want you to discourage you, because by the standard of American cities, that area would be considered better and safer than Pacific Heights in San Francisco or the West Village in Manhattan, so I guess everything is relative. However I just wanted to warn you that by Italian standards, that is not the absolute best area of Florence’s city center.