do I need a visa
No, as a US citizen, you won'tare already allowed into the Schengen Area visa-free, + as a family member of a Union citizen, you benefit from the same freedom of movement as the union citizen (as long as you are traveling with, or joining, the Union citizen).
However, as a non-EU citizen, you will need to apply for a residence card once in Italy. You have 90 days from your entry to apply for one.
An Article 10, family of union citizen, residence card (Carta Di Soggiorno Per I Familiari Del Cittadino Comunitario) is what you want to apply.
To do so, you must provide (source and full info) :
a) €16 revenue stamp
b)4 recent and identical passport-sized photographs
c) a valid passport - bearing an entry visa, where applicable - and a photocopy of its relevant pages (there is no need to photocopy blank pages)
d) documents confirming the existence of a family relationship to an EU citizen and, where applicable, a certificate confirming the status of dependent family member of an EU citizen
e) self-certified Statement of cohabitation (and of maintenance if the applicant is a dependent family member of an EU citizen) duly undersigned by the EU citizen who must state the full current permanent address where they live together under the same roof, along with a certificate of registration of the EU citizen issued by the Anagrafe (Registry Office of the municipality of residence). If the EU citizen is Italian, a photocopy of his/her valid identity document will suffice in lieu of the certificate of registration
f) up-to-date supporting evidence, if any, that the applicant is financially independent or that he/she is dependent on an EU citizen
g) the prescribed fee for all residence cards issued after 2nd August 2021 is €30.46. This fee can be paid for through post office help desks displaying the sign “Sportello Amico” by filling in the dedicated pre-printed paying-in slip.
You will apply at the Questura of your place of residence