You'll find through responses that each island has things that are unique and make the diving there great. Hawaii has a great deal of diversity and that is one of the many draws to diving here. You may want to express your areas of interest and what you are looking for. You'll also see that Hawaii has dozens of highly respected operators and well known DM/instructors. By researching here you'll see many of those companies and names of DM's that people rave about.
Kauai - Probably best known for the opportunity to travel to the remote island of Niihau and diving with the monk seals. Locally (off Kauai - chance to see some of the rare fishes that are otherwise only seen in the northwest Hawaiian islands. Niihau/Lehua is considered by many to be the best diving in Hawaii - but can only be scheduled with regularity in the summer.
Oahu - Recognized for some great wreck diving not as abundant on other islands.
Maui - Offers a great chance to visit Molokini, Lanai and Molokai as well as numerous Maui sites. Also vast shore diving. Molokini and it's current swept back wall is a famous Hawaii drift experience.
Big Island - Everyone who's opened a dive magazine knows about the famous Manta Night dive!!! The Kona Coast is also the calmest and clearest water of the islands more often than not.
These are offered as just quick examples and professionals on each individual island can offer better info but you get the idea...
World class turtles, lava tubes, moray eels, spinner dolphins, eagle rays, fantastic endemic life etc... can be found on all the islands.
Send me a PM if you end up having specific Kauai questions. Otherwise post individual messages specific to your island of interest and I think your responses will flood in.
Best of luck and the best of island wishes