Unfortunately the only option you have is a flight.
Israel is still in conflict with its neighbors to the north, Syria and Lebanon, so to get to Istanbul by land you will need to make a detour through Jordan, and even then you might have problems because apparently the Syrians don't allow entry if they notice any evidence that you've been to Israel.
The only ships going from Israel to Turkey are (afaik) these luxury cruises that cost a lot more than a flight, which is not THAT expensive.