I have been diving in the Eilat and Taba area, Nuweiba, and Dahab.
Nuweiba is by far the best destination for solitude and diversity underwater. There is not much to the town, but the diving is orders of magnitude better here than in Dahab or the Eilat/Taba area. So far I've made 5 trips to Nuweiba to dive with African Divers Nuweiba. The owners, Daniel and Sarah, are great people, great divers, and great dive guides. It is very uncommon to encounter another dive group underwater in Nuweiba, and I like this very much. I have seen the most in Nuweiba and I have seen it consistently. On one dive I saw 4 different species of nudibranchs, frogfish, octopus, cuttlefish, eels galore, crocodile fish, shrimp, cleaning stations, huge sting rays, beautiful soft coral, and the list goes on. This is not to say that such things cannot be seen elsewhere, but the combination of relaxed personal service, secluded dive spots, pristine habitat, and species diversity makes Nuweiba top on my list. You can also live like a king at a cushy resort for peanuts. Check out the Swiss Care or the Elaria.
There are a few treasures left in Eilat. I would avoid the Satir (the missile cruiser mentioned in the above post). I dove it yesterday and it is covered in a gooky green algae. The surrounding reef is also covered in algae and is in quite poor condition. Further south in Eilat is nice. Dive the lighthouse or the caves or down near the border. If you dive near the border expect crap from the Israelis but you can still dive there.
Aquasport runs a nice boat trip from their dive center in the Taba Hilton. The boat is nice and comfortable, the crew very pleasant, and the diving was excellent every time I have gone (about 6 days over the last 6 months). The price was reasonable as well. I believe it cost $99 for 3 dives, including tanks, weights, border exit tax, transport, and a nice hot lunch on the boat. Equipment costs extra but I lug mine around.
I like the town of Dahab but the diving sucked. I originally intended to do 4 days of diving, but I stopped after 2. Granted, if you've never been somewhere like the Red Sea you will probably think its amazing.
Have fun and watch out for tricky thieving bedouins.