I'm thinking Oahu and Big Island specifically, but if you have strong recommendations for snorkeling on other Hawaiian islands, I'll try to make my way over to those ones too!
For me, diversity is what I'm looking for, in fish, coral, etc. If turtles, dolphins, or other larger, less commonly seen animals are often sighted there, that's a plus!
On the Kona side of Big Island, a lot of companies offer daily a trip to snorkel or SCUBA-dive with manta rays at night. I guess you can also just swim there and join the party if you're unwilling to pay, but I don't think that's simple or safe to do, especially as this is a night activity.
I did a dive there recently and it was absolutely amazing, easily the best dive I ever did, and as the whole thing is pretty shallow and the mantas swim high I think the snorkelers get a great view as well. I later discovered it's considered one of the best dives in the world, and I wasn't surprised.
You can find a lot of YouTube videos of the diving experience, and I even found one taken from a snorkeler's perspective.
Also, while you're at it, on the south coast of the Big Island is a small but splendid black sand beach where turtles often come to rest - when we dropped by, for instance, there were 2 or 3. I didn't snorkel there but it is my understanding you often get to see them when doing so. The beach is called Punaluu County Beach Park.
You could always hit Molokini, off the island of Maui, which is a heavily traffic'ed snorkeling spot - great for spotting coral reefs. Plus the guided tours ensure that you are informed about what you see. Summers around Maui are great for whale spotting - though I seriously doubt you will get to swim alongside them :)
If this is your first time in Hawaii, I would strongly recommend a few days in Maui, not only due to the abundant snorkeling options, but a host of other activities as well.
We recently took a trip to Hawaii and went to Hanauma Bay in Oahu. It was a lot of fun. What I liked was that it had several different sections to the bay. The farther you swim out, the more wildlife you will see. The water was rough when we went so we stayed in the area closest to the shore, but I still saw a turtle!
The Kona side of the Big Island has the most extensive coral reefs in the main islands. "Two-step" just outside of Pu'uohonua o Honaunau has an easy entry and has an extensive shallow reef top. It is frequented by turtles on the South side (towards the Place of Refuge) and Hawai'ian spinner dolphins frequently use the bay as a resting spot (they are unfortunately chased and harassed by swimmers).
Alula Beach on the South Side of Honokohau Harbor is another excellent snorkeling spot, especially if you are a little more comfortable with snorkeling. There is an extensive reef top in 20-30' of water that is the home to large schools of fish, including pyramid butterflyfish, snappers, and Heller's Barracuda. Turtles are also common here. This is easy to snorkel / freedive and is such a nice location that most of the dive and snorkel boats will use it as one of their stops, even though it is literally only 100 yards from the harbor entrance and is easily accessed from land.
The reefs near the Captain Cook monument in Kealakekua Bay are excellent, but are generally accessed by boat or kayak, although there is a (long and hot) trail that can also be taken to them.
If you want an exceptional experience, the manta ray night dive / snorkel is, if the animals show up (which they generally do), is amazing. When certified SCUBA divers visit, I insist they do the dive.
