Florence in July, lovely! there is so much happening outdoors, I am sure you will have lots of fun.
Here are a few places that I have visited personal, and are in safe neighbor hoods. However, anywhere in the city center is pretty safe. Especially now with the extra protection for possible external threats, you will find that the police protection has increased. I always feel safe when I walk through the city, even in the wee hours of the evening.
Antiche Dimore Fiorentine: Boutique B&Bs in Downtown Florence
Villa Antea - Luxury & Timeless Elegance
Review by VisitFlorence: Palazzo La Medicea & Terrace Roof Top
Il Palagetto B&B - Parking in the City Center
A Review: Residenza d'Epoca Toscanelli - In the Middle of it All