Eilat sits directly on the Red Sea but from the culinary viewpoint, for reasons that I have never been able to understand, it might as well be located in the center of the Gobi Desert. In other words, to a large extent, Eilat has been a culinary wasteland.
Mike's suggestion for Giraffe is a good one but keep in mind that this is precisely the same Giraffe as you will find in Tel Aviv and other branches. Certainly nothing here that reminds one of the Mediterranean or the Red Sea.
The Last Refuge is always sort of fun. Nothing at all complex about the fish and seafood offerings but generally tasty and in a pleasant atmosphere. At about the same level (if it is still open) is Pago Pago which also offers simple fish and seafood offerings and a charming view of the lagoon.