It's been a few years since I've tried it and I don't know if this still works, but check out cheap flights to CAI, then hop over to TLV on a cheap airline. I've tried El Al and Air Sinai on this hop. El Al was expensive and much more comfortable in the air, but Air Sinai was cheap and vastly easier on the ground in CAI. I had to book the Air Sinai in a CTO in Cairo. But at least I spent a couple days seeing the Cairo Museum and the pyramids.