I have one spot, but it's pretty much snorkeling only (maybe 15-20 feet in the deep spots) - the Waikiki MLCD. Go to Queen's beach in front of the zoo, go out towards the wall on the right past the swim buoys, and follow the reef edge around toward Diamond Head. It's VERY shallow on entry, vis is only decent on the outside and is abysmal if there is any surf. A flag is a very good idea. LOTS of fish, and the only place I see lots of 'omilu (bluefin trevally) and barracuda. Look out for morays as well. The reef edge is uncovered during some low tides so the only real entry and exit is toward that wall, unless you swim all the way around and re-enter at the Sans Souci channel.
This is kinda my secret spot, lots of people snorkel on the inside but very few go check the outside. It's walking distance from pretty much all the hotels, which is a plus.
Another area is Kahe Point on the leeward side. A flag is very important here as tour boats visit the area frequently, as well as many fisherman of all stripes. You can go out from the beach and head South along the shallow reef, or otherwise there are various areas that are at a better scuba depth offshore. If you google it, there are several good websites which give you more detailed shore diving info. The reef is VERY healthy compared to Waikiki (which is mostly dead), but unfortunately the fish are not as impressive - if it's good to eat, it's been fished off the reef. Lots of sergeant majors, black triggers, manybar goatfish, and butterfly fish, but not many surgeonfish, parrotfish, or predators.
Otherwise, I would say the South shore is calmest at this time of year. North will be mostly off-limits, leeward (west) and windward (east) variable. Check the surf reports before going out for sure.
**Quick edit/reminder - the Waikiki MLCD is a Marine Life Conservation District, like Three Tables or Hanauma. No fishing of any kind.