Hanauma Bay, not far south of Waikiki is by far the most-visited snorkeling venue in the Islands. But that doesn't mean it's a must-do. It can be crowded and the visiting protocol is a hassle—plus the snorkeling isn't that great close to shore. Two nearby alternatives are Makai Research Pier (at the peninsula in the photo above), and little-known Cromwell's Cove.
Makapu'u Beach Park (above) is on the way to Makai Pier, a spot to enjoy a dreamy picnic and watch surfers. The pier is where the yellow submarine manned by crews from the Hawaii Underwater Research Lab (HURL) expolore offshore waters. You can easily swim from shore amid sea turtls and schools of colorful fish. You can walk out the pier beforehand to scope the scene.
Cromwell's Cove is a really cool man-made enclosure set right below (I mean there it is!) the Shangri La Mansion of the wealthy socialite Doris Duke. (Cromwell was her husband.) The parking for the cove is in a suburban neighborhood, and a walk with a short rock-hop is required. Only high school kids frequent this place (making weekdays a better choice for solitude). This photo is taken from steps that lead into the clear water. From the same parking, you can also walk right (Crowell's is left) to Ka'alawai Beach, which is the strip of sand you can see just above the wall in the photo.
Oahu Trailblazer has more deets on these places and all the other spots to find quiet, beautiful spots on Oahu. Surprisingly, populated Oahu has more undeveloped beaches than Maui.