The Red Sea. Two very good places to set out from are either Sharm el Sheikh, Egypt (Sinai Peninsula) or Eilat, Israel.
There are hundreds of different dive sites and many dive companies in each of these towns to take to out there. The Red Sea offers some of the clearest water that I have ever dove in.
Sites range from reefs, caves, and caverns; to sunken WW2 transport ship, sunken submarine; to coral fields.
The reef, corals, and fish are all strictly protected by the goverment there to keep divers from damaging anything. This helps to keep everything intact for years to come.
This is where I learned a lot more about diving and made a great deal of dives. If you can afford the trip, it is well worth it. I was lucky enough to have the Army pay for my 1 year stay in Egypt, so the diving was the only part at my cost. I still have my dive logs and videos around here somewhere.
Lots of sea turtles, hammerheads, whitetip reef sharks, blacktips, rays (many different species), triggers, etc.