Lawrence T,
I have lived and dived in the Naples, Italy and Athens, Greece areas over the past 30 years or so. I was in the Navy in Naples in the mid 70s and in Athens in the early 00s. The water is warm in both places in the summer, but there is NOTHING to see. The Med is pretty sterile. When we got to Athens, we were advised to ask the price of a seafood dinner in most restaurants because you were likely to pay up to $100 for a meal because the fish was all imported. I paid up to $70 and got nothing special.
If you can get to Sharm El Sheikh in the Red Sea, you will see all the fish and coral you want to see. An amazing place. Go with Red Sea Diving College there. They are a class act.
With that being said.....I am an instructor and was diving almost every weekend in both places. I love being underwater and the water is warm and usually clear in the summer in the Med, but there just isn't much to see. In Greece, the "Scuba Police" keep you away from the antiquities, so that limits diving. If you do try the Greek Isles, be sure to check on-line to ensure diving is allowed at that particular island.
Good luck with your trip. I understand there are some neat sites up in that area, but they will be cold. But that is what wet/dry suits are made for. Let me know what you decide to do.