My main reason for choosing the Big Island! --- I heard the snorkeling there was the best in Hawaii. It certainly was not a disappointment. We rented a kayak and paddled ourselves to Kaelakekua Bay---it was nice, but not really nicer than many other places that are easier to get to. (My husband still thinks I was trying to kill him with the kayaking!) Our favorite place was by the Place of Refuge (Honaunau Bay)---deep and somewhat tricky to get into, but great. It was here I first experienced the cool water springs coming into the ocean water. THese pockets of water had a way of really fouling up vision through the mask! At first I thought they were fogging up, then realized it was the fresh water somehow sticking to them. A wipe with my hands usually cleared it up until the next blast of cold water. We also liked Kohaluu for it's close proximity to our resort and great variety of fish, plus it had a nice beach for the Kona area. We went there almost every day. We also really enjoyed KAUNAOA BEACH (MAUNA KEA BEACH). Snorkeling on the left side of the bay was great. There was a large reef there to attract a lot of fish. The rest of the beach was beautiful to look at, but not good for fish gazing.
We did see alot more yellow tangs here by the Big Island than around Oahu and Kauai. They were being snatched up and sold to aquarium dealers until the last couple years. Now that's illegal and the numbers we saw here by the Big Island were pretty impressive. We also saw many turtles all around the Big Island, as well as the several varieties of fish: parrot fish, trumpet fish (both yellow and gray), wrasse, pufferfish, soldier fish, surgeon fish, different species of triggerfish, as well as a few different species of eels, a couple octopus, and several more kinds of fish that don't come to mind right now.
Don't forget to get some defogger and use it. It really does make a huge difference. Also, don't forget to get and use sunscreen, the sun will burn you much quicker there than on the mainland. I found Bullfrog to be the best sunscreen I've ever used. An underwater disposable camera is fun to have while snorkeling, too. They really do a good job in the crystal clear Hawaiian waters.