I lived on Oahu for 6 years. Hanauma Bay is, by far, the most popular snorkel spot. But I really just think that's because it's close to Waikiki and is promoted as such. If you're entering from the beach, you have to get WAY out there to see any type of coral. Nearly the entire bay is destroyed. The fish will swim in, but there is no coral to be seen until you're practically out of the bay.
Shark's Cove has been mentioned.
Not sure how long you're on the island. If you're there more than a week, you really need to make it to another island. Kauai or Maui. In my opinion, much more of the undisturbed beauty that is Hawaii.