re: Traveling and safety in Rome and Florence

We (husband, me, 3 elementary aged kids) visited both cities in July, walked pretty much everywhere, and always felt safe. We stayed in apartments rented via vrbo or FlipKey. In Florence, we were across the street from the Academia. In Rome, we stayed in a residential area right by Piazza Navona.
The only really sketchy area I remember encountering was the area immediately around Termini train station in Rome. I wouldn’t have felt comfortable staying there.