I would suggest:
Northshore:
- Haleiwa Town. Great community, surf town, laid back.
- Kono's and Haleiwa Beach House are two great places to eat.
- Matsumoto Shaved Ice is an institution and a MUST!
- Dole Pineapple Plantation Tour if you want to learn about the history of the island plus all the pineapple juice you can drink
- Alii Beach is a super cool place to catch the sunset. I think also it is a spot that was commonly used to film Baywatch back in the day so let us know if you spot "The Hoff" lounging around! ;P
Honolulu:
- Kona Coffee Co./B. Patisierre - Hawaiian coffee can hang with some of the best beans in the world! B. Patisierre is a new location of a baker in San Francisco. The pastries are like you are in Europe! No joke. Owner was trained in Paris and here is SF her store has a line ALL DAY!
- Ala Moana Shopping Center is always popular if you like shopping malls
- Side Street Inn (close to Ala Moana Shopping Center) Probably the worst kept secret but it's where many of the islands best chef's go to grab a meal and unwind.
- Alan Wong's - Make reservation. Upscale and nice place to go for date night.
- Pearl Harbor : BOOOK TIX for USS Arizona Memorial EARLY as it tends to sell out. Truly a moving experience even if you have no affinity toward WWII.
-Hike Diamond Head - nice hike and great views.
Hanauma Bay - good place to snorkel and hang on the beach BUT go early as this place gets crowded.
Waikiki - as previously stated a total tourist trap BUT if it is your first time in Hawaii, go to the historic Moana Surfrider/Westin Hotel in the late afternoon. Grab a table beachside, order a drink (or two), watch the sunset! Forget everyone, and everything else going on and take it in. Drinks can be pricey, but you are on vacation! You really only need to do this once, but you will have experienced Hawaii. Afterward, then you can get sucked in to all of the touristy stuff...
Dress is super casual all the time: t-shirt/shorts/flip flops. If you go to a nice dinner a button down Hawaiian Shirt will do.
Hope this helps and wish you safe travels. Aloha...