Consider St. Vincent and the Grenadines.
Getting to SVG is easy if you don't mind a hop via Barbados (LIAT, Air Mustique and SVG Air provide service from Barbados).
SVG is made up of 32 islands, St. Vincent being the largest with over 25 miles of leeward coast and only 2 dive shops), the inhabited islands of Bequia (2 dive shops), Mustique, Canouan and Union Island (1 dive shop each) also have some great diving, and are accessible by local ferry from the main land or twin props from Barbados or St. Vincent.
Accommodation on each of the islands varies from very high end, to small beach front family owned hotels, and self catering apartments.
The best diving is to be found in St. Vincent, primarily due to the volcanic nature of the geology and very well protected leeward coast, I would liken it (for the most part) to diving in an aquarium. A huge variety of fish species, over 250 in the last REEF survey, diverse critter population, pristine reefs of hard and soft corals with some pretty wrecks and stunning wall dives (especially in the north leeward) make this island an touched treasure.
Bequia may be best suited to your needs as there is a wide selection of rental properties within walking distance of the 2 dive shops. The diving in Bequia can be a little more challenging as the island is much smaller than the main land, and it does not have a distinct leeward coast, however it more than makes up for this with some very pretty drift dives. If you would like to see bigger pelagics during your visit, Bequia is the place.
Union Island is your gateway to the Tobago Cays, a marine park made up of uninhabited islands, which featured in the first Pirates of the Caribbean movie - Captain Jack was marooned here! Mayreau Gardens in the Tobago Cays is one of the prettiest drift dives ever.
SVG is not the most easy destination to reach, however if you want world class diving, tiny dive groups usually (2 to 4 divers per boat) and an off the beaten track dive vacation I guarantee you will not be disappointed.