Is tap water safe to drink in Italy?

Completely, and Rome's is famously good. The public fountains you'll see running constantly in Roman streets — the little nasoni — are drinking water, and locals fill bottles from them all day. Carry a refillable bottle and use them; it saves money and a great deal of plastic. In restaurants you'll be brought bottled water by default and it's normal to accept it, though asking for acqua del rubinetto is not offensive. The only place to be careful is a tap marked acqua non potabile, which means not drinkable, occasionally found in older buildings and on trains.