Do not look for nonstop flights; they can cost 50% more than stopover flights, if not more (my guess is $1500 from NY instead of $1000). Look for discounted flights from any important European city to Israel and then connect with the best of them by booking a discounted flight from New York to that city. Allow several hours to change flights and don’t be afraid to stay over for many hours.
I’ve assumed that you would be taking off from NY, but the same goes for any N. American city that flies to various European destinations. Good luck.