Citizenship does not matter much. It is more a question of where you have been. Where are you travelling from and to?
Persons RESIDENT in the United States (not necessarily U.S. CITIZENS) are allowed to CONNECT FLIGHTS at an Italian airport in order to arrive at their final destination OUTSIDE of Italy, provided that they do not "enter" Italy (getting an entry stamp on their passport) AND remain within the restricted area of the Italian airport where they are connecting flights.
Nevertheless, persons RESIDENT in the United States who have E.U./Schengen CITIZENSHIP, and their family members, ARE allowed entry into Italy for any lawful purpose (including tourism), BUT are subject to a 14 period of self-isolation in Italy upon arrival, UNLESS arriving on a "COVID-tested" flight such as those from JFK or ATL to FCO or MXP. Additionally, persons who "have a proven and stable emotional relationship (even if not cohabiting) with Italian/EU/Schengen citizens or natural persons who are legally resident in Italy (long-term residents), who need to reach their partner's home/domicile/residence (in Italy)."
may also enter Italy, always subject to the period of self-isolation described above (unless arriving on a "COVID-test" flight.
United States residents are also allowed entry into Italy (subject to 14 days of self-isolation) for the following narrow purposes:
return to one's domicile, home, or residence.
There are several additional exemptions from the self-isolation requirement:
BEWARE: Persons (including U.S. residents and citizens) who have stayed in or transited through BRAZIL in the previous 14 days are BANNED from entering into or transiting through Italy, except as provided in the Regulations:
The foregoing is likely to change in the near future, as Italy is EXPECTED to open up to tourism from abroad (including from the United States) for those having been fully vaccinated or having a negative COVID-19 test result performed no more than 48 hours prior to entry into Italy. We should learn of the particulars before the end of May.