I will help you rather than send you on a Google chase..

You will be arriving into Terminal 3 (right in the middle of the airport terminal buildings), if flying from the USA. The terminal that they will land in on Alitalia may be Terminal 1, 2, or 3. But, if they are arriving on an international flight not from the European Union, they will also arrive in Terminal 3.

I suggest that you meet just outside of the Information office after you exit from Italian Customs. There are many chairs just outside of that office with a cafeteria just across the hall from it. You will be on the ground floor of the terminal building.

Bear in mind that for your return flight, you will also check in on the second level of Terminal 3 but will then need to take a Fumicino shuttle bus to remote Terminal 5 (for all flights to Israel and USA.).

If, the night before you return home, you need to stay at the airport I highly recommend the FCO Hampton Inn. It has a great restaurant that is reasonably priced, free Internet, and shuttle service (10 minutes) every 30 minutes, and is $100 cheaper than the Airport Hilton...where I also stay frequently.