I've dived Kauai, Maui, and The Big Island--and the Big Island is hands down my favorite. I has more sites, lots of diversity, and generally better conditions. It also offers the opportunity for night diving with mantas and black water diving. That said, all the islands have their charms Maui has the Carthaginian wreck and back wall of Molokini, In the summer Kauai offers an opportunity to get out to Nihau.
To my knowledge, there are no dedicated dive resorts in Hawaii. But there is the Aggressor.
In Kona, there are several good dive ops, but my favorite is Kona Dive Company. Family run, and a top-notch staff that offers valet service. The offer the manta night dive and they offer 3 tank long ranges more often now that they have another boat. Ther marina is about a 12-15 minute drive from downtown, so I suggest renting a condo in that general area. We like the ocean front units at Kona Bali Kai, and that adds another 5-10 minutes to the drive time. Dive with them once and you really do get treated like family. The only thing they DO NOT offer is the black water pelagic dive. If that is your thing, it needs to be arranged with another op like Big Island Divers (also great).