Orbitz – LINK
Priceline – LINK

You can currently snag tickets TLV-JFK on Alitalia airlines with 1 stop-over for just $792 round trip. There are also some select flights available for $715, though most price out at $792.

Dates available for these fares are from January 8th through April 6, 2014. As long as you leave before April 6th, you should be able to find these low fares even though you are returning after April 6th. For example, A flight leaving April 3rd and returning April 29th is currently only $792.72 round trip! Passover is April 14th through April 21st, so this is perfect for those wanting to spend pesach in the US.

Tickets can be booked on Orbitz or Priceline. With Orbitz, you can cancel your ticket free of charge till 10pm CT the day after your booking.

With priceline, you can cancel your ticket free of charge through 11:30 pm the day after you purchase your ticket.

(Thanks Eli. L. For the tip!)