You can currently get snag tickets NYC-TLV on Turkish airlines for just $684 round trip.
Dates available for these fares are mid January through March 10th on the out bound and from the beginning of February through the end of march on the return.
Turkish airlines is part of the Star Alliance network. Also, a nice thing about Turkish airlines is that they still offer 2 free bags.
With priceline, you can cancel any tickets you purchased through 11:30 pm the day after you purchase your ticket. These fares “also seem” available on Orbitz, but in reality they are not bookable there.
(Thanks GS for the tip!)