I've been living on one of the less populated, less touristy Hawaiian Islands for a few years now. I go to Oahu mainly for business but I spend an extra day or 2 sometimes especially if I know someone who happens to be there on vacation. If you are looking for off the radar here is what is suggest.
Food
Sansei - sushi place in east Waikiki (think it is in or beside a marriot) Half price sushi menu after 10pm on Friday and Saturday night, 21 and over only after 10pm, bar like atmosphere with Karaoke but you can sit outside to get away from the noise. Extremely good food for the price. Panko crusted ahi roll is great and always on half price menu.
Sidestreet Inn - hole in the wall place on a one way street a few blocks from Ala Moana mall. Serves local style food. Great fried rice and garlic chicken
Marukame Udon - There will be a line of Japanese tourists down the block but it moves quick and is really good and really cheap. Its located on Kuhio Ave in Waikiki
Nico's at pier 38 is also good and inexpensive for lunch or dinner its located right next to the fish auction so they have a new menu everyday based on what is available
Eat some Poke. Its just raw fish (usually ahi) mixed with a sauce and seasonings. Don't have to get it from a restaurant, any grocery store deli/seafood counter will have it
Activities:
I recommend a sunset booze cruise off Waikiki over a mid day snorkel trip. A flat rate gets you a few hours on the water and includes free drinks. Better deal than paying $6/beer in a beach front bar.
Lanikai beach on the east side of the island is the best beach on the island. Not sure if its on the map but if you go to Kailua beach park you're in the right area. There is a trail that goes up a small ridge in the neighborhood behind Lanikai that gives some pretty great views and if you follow it far enough it leads to some old WW2 era pill boxes.
I've heard the polynessian cultural center has a great luau show but it is run by the Hawaii BYU campus which means they do not serve alcohol.
Hanauma bay is a tourist trap, all the coral is dead due to the thousands of people stepping on it daily, there is a fee to get in, a line to pay the fee, a video you have to watch before you can go to the bay and a line to watch the video. Rent some snorkel equipment for a few bucks a day at any of the hundred places on the island that rent and ask for a map of good spots you'll get plenty of spots with the same fish and way less people/hassle of Hanauma bay. Sharks cove as mentioned by others is a good spot.
Most of the stuff I've recommended is easily done if you are staying in Waikiki or the south side of the island. If you stay on the north shore a lot of this stuff will be a hassle due to distance and the 3rd worst traffic in US but the north shore is great especially in summer when the big waves aren't rolling in so you can actually swim and there aren't huge crowds to watch the surfer. I could go for awhile about the weather patterns, the wind and ocean conditions but i'd just advise you find a good website and read up on it, most of the info you pay for in a guide book can be found online for free. Also be advised most 'off the radar' beaches, waterfalls, streams, valleys, etc. will have a Hawaiian name, an English name and sometimes a local slang name, its easy to get confused and another great reason to read up things.
