The Red Sea near Aqaba has a host of places to dive, for all levels. I was most taken by diving around a shipwreck. It was eerie to see such a foreign object suspended in space and slowly being taken over by sea life. There are several ships you can dive around, and a tank. There are many outfitters to take you diving; I'd find one either by reference from your local dive shop in the U.S. or by using a local tour operator. Be sure to do some googling of the various dive sites before you go, otherwise it will be much too hard to decide on a spot where you'd like to go. If you're an avid diver, you could easily spend two or three days diving.
The highlight of my dive was seeing my absolute favorite sea creature—the nudibranch!