Hi Bill,
I've been to Eilat a bunch of times. For accommodations, there are some inexpensive choices. First is the Adi Hotel. It is fairly modern. Nothing too fancy, but good for the money. The location is short walk up the hill, not far from the airport & central bus station. The shopping mall is only a 5-10 minute walk downhill. So if you want to get prints made on a Fuji Frontier minilab, no problem. I paid about $50 last year. http://www.adihotel.co.il/index.php?lang=en
In 2003 I stayed at the Moon Valley Hotel. It is located toward the rear of the marina area. It is much older but still a nice value.
Eilat has a bunch of good dive operators. I like Aqua-Sport. They are right on the beach. Red Sea Sports Club, Marina Divers, Lucky Divers and Siam Divers are the other ones. Aqua-Sport's website is http://www.aqua-sport.co.il
My favorite site is Moses Rock. It is a coral head in shallow water. The hard corals are healthy and there are a few red soft corals. Understand that you won't see too many soft corals in Eilat. The reef is covered with anthia fish.
Another good site is the wreck of the Satil. It doesn't have as many fish as Moses Rock, but it is one of the few places where you can see good soft coral growth. If I had one day, I would do the Satil in the morning followed by Moses Rock.
Japanese Gardens is promoted as the best site. I disagree. The topograhy is interesting but Moses Rock has better corals and fish. I did have a nice encounter with an octopus once.
If you have more time, do some day diving in Taba, Egypt. The diving in front of the Taba Hilton is great. You cross over, do two dives and come back before dinner.