Icelandair or Play (a budget carrier) have round-trip flights from New York/Newark (JFK/EWR) to Reykjavik (KEF) for $251-$410, NONSTOP. Flights September to February. Extended weekends available.
Some small OTAs on Skyscanner and Google have this for 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).