It's possible to snorkel along the stretch fronting Kapiolani Park (the Kaimana Hotel and San Souci beach which is just to the left of the Natatorium) but it's very shallow, say, an average of 6ft and not more than about 12ft. If there's any kind of waves, well, poor viz and rock-rash is no fun. Just about anyplace else, I'd be afeared of loose surfboards, loose tourists, and canoes. Yeah, some really rotten surfers may intentionally try to "skeg" you (i.e. slice you with the surfboard's fin) but that tank on your back is a deterrent as is that samurai sword strapped to your calf. But anyway, as a practical rule, if surfers are there, you shouldn't be.
On the plus side, periodically (alternating years?) there's a total ban on fishing and if you get in at the right time, you'll get to see a lot of fish that might not usually be seen. On the western end of Waikiki, near the Halekulani and Hale Koa, there occassionally have been extremely close inshore sightings of baby hammerheads (1 to 2ft long) during the pupping season, usually beginning from early summer. Fairly harmless but very very exciting.
Contact or drop by the Waikiki Aquarium; they might have better tips.
