Finnair, Iberia, British Airways, American Airlines and various other airlines have round-trip flights from Seattle (SEA) to Rome or Venice (FCO, VCE) for $610-$641 with a connection. Flights February, March, October, and November. 7-day minimum stay required. Dates over Thanksgiving are available.
A Carry-on bag and also a personal item is allowed for free on American. You can avoid paying for seat selection by accepting the randomly assigned seat at the gate.