That is the historical center - via Guelfa has a lot of shops and foot traffic at all times of the day given its closeness to the Mercato Centrale, there are a lot of smaller side streets I would avoid on my own at night. I would keep to the better lit streets (as you would anywhere else in the world) if I was alone and always be aware of surroundings. While there are incidents of petty theft/robbery/pickpocketing, I would never say I've ever felt Florence to be dangerous - and I've walked the center at night and alone and always seen people out and about on the main streets so have felt safe.