The short answer is yes. Drinking water from the tap in Italy is considered safe.
Tap water in the major cities and towns around Italy is safe for consumption, and there are thousands of old-style water fountains dotted around cities, like Rome, where you can fill up water bottles. Some very rural areas in Italy may have water that is not safe to drink. If there is a sign reading ‘acqua non potabile’, this means that the water is not safe to be ingested.
If you wish to drink purified water, bottled water is abundantly available in stores, especially in tourist areas. However, be aware of your environmental impact when purchasing water in plastic bottles, and consider filling a reusable bottle or canteen with water from your hotel for your day of sightseeing instead.