There were a bunch of places that I wanted to dive in Hawaii while I lived there, but I never got around to them. Oahu has some awesome diving, but most of the spots are not on any commercial itineraries - too remote or maybe a little too hairy for most divers.
I did some great dives on Molokai from Kaunakakai to Laau Point - the sea cliffs on the Kaluapapa side looked awesome but are probably diveable only on a handful of days each year. No one gets out there much.
I managed to shoot 7 tons of bullets at Kahoolawe during one long day of Naval Gunfire Support training, but I never got to dive there - I knew some guys who did bomb clearance who had a ball diving in those waters.
When the village of Kalapana on the Big Island was eaten by lava, I ran into a guy who was shooting the offshore lava flows for National Geo I think. That sounded pretty cool. He got sucked into an underwater downdraft and went from 20' to 180' in seconds, but he knew what he was doing so he was ok.
I would pass on some of the stuff Chris Newbert did diving down the FAD buoys offshore at night to 200' to see what came up to see him. Even I have my limits now.
I know that none of this helps you - you're looking for dive operator recommendations. There's good ops on all the islands.
For a tourist, go for Maui or the Big Island Kona side. Kona I still recommend Dive Makai. Plus both islands have a Costco which might come in handy or not.