Norwegian has cheap flights from JFK to LGW, especially if you pay in British pounds (ht: Theflightdeal). Easyjet has cheap flights from LGW to TLV. Both are budget airlines, so everything is extra. If you choose this way, travel light.
Example for NY yeshiva vacation week (note long layover in London on return trip, and return is on Monday).
Norwegian lv JFK Jan 21 at 22:30 (motzai Shabbos; shkia is 17:00), ar LGW Sunday 10:00
Easyjet lv LGW 12:50 ar TLV 19:55
return
Easyjet lv TLV Jan 29 at 20:50, ar LGW at 00:25 Monday
Norwegian lv LGW at 17:10, ar JFK 20:30
Total is GBP 302.30 for Norwegian, GBP 142.98 for Easyjet. That's less than $550.
Go to norwegian.com and easyjet.com to book.