The British Virgin Islands is probably the easiest place to go diving from a cruising yacht. The water is normally very clear and the country has worked hard to preserve it's reefs.
There's a Marine Park mooring system in place, which places moorings at all of the dive and snorkelling sites around the BVI. In 2012, there were 66 locations with moorings which are all strong enough to take a 50 foot yacht - in some locations, there are multiple moorings available. There are three colours of moorings - red for general use, yellow for commercial use only and blue for dinghies. You can pick up any red mooring with your yacht. In 2012, it cost $50US per week for the mooring permit.
That's the good news. The annoying thing about the mooring system is that the majority of the good dive sites have yellow commercial moorings and, in most locations, the red moorings are only of use for snorkelling. This means that apart from the more popular places (like The Rhone and The Indians), you have to make use of yellow moorings. We adopted the strategy of picking up a red mooring with our yacht and then tying our dinghy with a long painter to a yellow commercial mooring to make the dive. At least this way, a commercial dive boat can pick up the same mooring.