Icelandair has round-trip flights from Newark/New York (EWR) to Rome (FCO) for $408-$423 with a connection. Flights in November, January, and February. Departures on Tuesday, Thursday, and Saturday. No Thanksgiving dates.
Some small OTAs on Skyscanner and Google have this for as low as $377; cheaper than the airline. If you plan on booking there, beware of any site that charges a fee to cancel a ticket within the 24-hour “free” period. Use unknown booking sites at your own risk.
A Carry on bag (20-lbs @ 21.6 x 15.7 x 7.8 inches) and a personal item (15.7 x 11.8 x 5.9 inches) is allowed for free on Icelandair. You can avoid seat selection fees by accepting the randomly assigned seat at the gate.
Icelandair offers free stopovers, which good if you want spend a few nights in Reykjavik. More details are on their website (link).