Where you eat is not as important as what you eat. Because your in a culturally diverse environment you will be bombarded with new sights and smells. To make the most of your experience, try everything at least once.
Here is a list of my favorite Restaurants. They are not fancy but you will see plenty of locals enjoying the food and thats always a good sign.
If your going to Hawaii you have to try some hawaiian food. Thats kind of an eclectic mouthful since most of hawaiian food is a combination of Japanese, Chinese and Filipino along with some western influence. But with all that influence it's still uniquely Hawaiian.
Poi
Gotta try it, didn't say you had to love it. It taste like school glue. Don't ask me why I know this. Its supposed to be bland because they used to eat a lot of salted meats and the poi would mellow out the salt. (My Wife thinks it tastes like watery carrots)
Poke
Fresh, and by fresh i mean raw fish, seaweed, green onions and other secret ingredients. It tastes better than it sounds.
Taro
Very similar to a potato but purple. It doesn't matter how you have it, just try it. Any thing thats abnormally purple has tarrow in it you can even order a tarrow turnover from McDonalds, thats not a typo, they don't have the apple ones.
Spam
Back to McDonalds for some Spam and eggs for breakfast. They really serve Spam at McDonalds in Hawaii!
Spam Musubies
You can order any type of musubies but Spam is the best. Its a giant Spam sushi. Imagine a slice of Spam on top of about 2 inches of rice with some secret sauce in between all wrapped in norie (see weed). This is so ONO (delicious).
Manapua
This is steamed bread with marinated meat in side. The bread is lite and airy and the meat is heavily marinated. The bread tastes a lot like pizza dough. My favorite are the Char sue ones. Its a red pork.
Shave ice
Please don't say shaved ice, some one will slap you. Its not the same. Shave ice is less grainy than a snow cone. Go to Matsumotos in Haleiwa its worth the drive and get it with a scoop of ice cream. If the line is too long, the guy across the street it pretty good. (or just wait, it moves fast)
Malasadas
Get them from the truck. Leonards makes the best, and they send a truck to different parking lots for the day. If you miss the truck, their shop is down town Honolulu. Click here for a list of the parking lots they will selling from.
Dried Li hing Mango
The Lihing spice is a delicious blend of sweet and earthy almost bitter flavors. Its on a lot of fruit so try anything Lihing
Kalua pork
I put this down the list a ways because I'm assuming you already know what it tastes like. If not go get some.
Lou Lou
Steamed pork wrapped in ti leaves. Not the tea you drink these leave are like small banana leaves and when they are cooked they taste a lot like spinach.
BBQ chicken
Teriyaki chicken or BBQ its good no matter who cooks it. But you need to try it. Just because you have had chicken before don't think its the same as what you had back home, its not.