I go to Hawaii twice a year and Krustofky is correct, there are no true coral reefs in Hawaii. the reefs there are lava hard top with coral growing on it. What that means is the reef is old lava, not coral skeletons. That doesn't mean you wont see coral, but the coral are individual heads, or are groups of coral heads growing on lava not old dead coral. Below is a typical scene, rubble and rock with coral head on it, sorry the photo is so blue, we were deeper then 100 ft most dives and I was too far from the coral head for a flash to show color
here is a photo from an earlier post that shows a large group of corals, so big you don't see the rubble under it, but it is there
In the summer the best places to go to swim are on the north side of whichever island you choose. The wind direction makes the south hare to swim or boat, but great for surfing, in the winter it is the exact opposite so you want to dive the south in winter. This doesn't matter for protected bays such as at Hanauma bay which is a great popular and highly recommended spot anytime of year if you are on Oahu. The northern parts of most islands are also always less crowded unless ther is something going on such as a surf tournament at Pipeline for example. No matter where you stay, remember except for the big island nothing is thta far away, on Oahu for example from Wiakiki nothing is more then an hour and a half away.
I know you said you didn't want to do touristy stuff, and you may not even be on Oahu, but if you are on that island and you have time go to the Dole Plantation. There is a lot of native shops there for instance the Koa wood store, plus other shops and they have a great garden containing many rare and endangered native plants. There is a painted gum tree right at the entrance which is worth the trip, it looks like someone threw pastel paints all over it, below is a photo of the bark
Where ever you go have fun, it is a great trip
