Serious Eats - seriouseats.com

Also, when you are on the Big Island, you want to eat "Plate Lunches" which are sort of like the Hawaii equivalent of the Japanese bento box. Local eateries / delis feature these things and they are great deals. These can include Korean bulgogi and the "Loco Moco" which originated in Hilo on the Big Island -- its a big hamburger topped with a fried egg and a brown gravy, served with rice. Cafe 100 in Hilo is said to be the originator of the dish

Another Hawaiian original is Saimin Noodles which is similar to Ramen but uses a very lightly flavored fish broth rather than a soy broth.

http://en.wikipedia.org/wiki/Saimin

Also on Kona and Maui you should be able to find the Lappert's Hanapepe Ice Cream Man ice cream shops. Its a very superpremium ice cream that uses local ingredients.

http://www.lappertshawaii.com

I'm not sure how up to date they are now, but eG's Hawaii forums (http://forums.egullet.org/index.php?showforum=128) has a big backlog of local joints that were reviewed that many are probably still in biz.

The guy who ran that forum was Sun-Ki Chai, a professor at the University of Hawaii and a major league foodie. His contact info is here

http://www2.hawaii.edu/~sunki/

Look him up and ask him where all the good places are. Tell him I said hi. :)

On Maui, Hanafuda Saimin won a James Beard award, for what that's worth...I'O is a hot, stylish place with produce from its own local, organic farm. Girard's is pricey and super-nice, uses mostly organic and is considered the best food by a chef friend of mine. Roy Yamaguchi has Roy's for the best fish. Des Amis in Paia, Maui has great tasting savory crepe meals for under 10$ and Hailemaile General Store also won a JB award years ago, though when I ate there, my food was cold, bland and carelessly prepared though I loved the restaurant ambiance. Have fun!

Uh . . . have to admit I am not really that knowledgable about the neighbor islands. Especially not Maui/ However, I did live in Kona for a while several years ago, and have been back to the Big Island a number of times, so I guess I can say something there.

I would second many of the recommendations that have only been made above. In addition, on the Hilo side, one restaurant that is particularly popular with the locals is the Seaside Restaurant and Aqua Farm, which has been in the family for 50 years, serving fish that have raised on their own premises. The ti leaf-wrapped steamed mullet and fried aholehole are signature dishes, while the "seaside chicken" is a pan-fried artifact of old-time local "American-style" food. Cafe 100, is responsible for popularizing "loco moco", the local gross-out of hamburger patty, fried egg, gravy, whatever else you can think of on top of a rice bowl. This is the Big Island's major claim to junk food fame, so you naturally must try it. However, rather than the ordinary moco, I'd recommend one of the deluxe ones, preferably one with both Spam and Portuguese Sausage in addition to the hamburger. As you're coming in from the airport, you probably pass right by Ken's House of Pancakes, where you can be like (some) locals and have saimin, oxtail soup, or tripe stew for breakfast.

On the Kona/Kohala side: If you are staying in the Waikaloa resort complex and dining upscale, Merriman's is probably the island's best-known "Hawaiian Regional" restaurant, and there is an outpost of Roy's as well. For more mid-range restaurants, Kirin in the Hilton Waikaloa is a decent pan-Chinese (though expensive compared its other branches). The local branch of Alan Wong's is further south, in the Four Seasons Hualalai resort. . Otherwise, good luck getting out - it will take you a good half an hour of hiking to the parking lot and driving to see anything much other than lava rock and sunburned folks in matching aloha shirts.

Kailua is the "metropolis" of Kona, but since the original Sam Choy's Kaloko closed, there is no single place that stands out. O's Bistro seems to be picking up the "family n' fusion" mantle from Sam Choy Kaloko, serving fancy versions of plate lunch and saimin. Off Ali`i Drive (the main drag), Cafe Sibu is has long been popular for its very casual Indonesian, and Huggo's for its pricy seafood (they have a casual offshoot next door). For classic plate lunch, there are a lot of choices, but Kona Mix Plate on Palani Rd. is probably the biggest name.

If you get to coffee country, one big recommendation is to eat at the Manago Hotel's restaurant, and to stay there, though it is definitely not a luxury hotel. The restaurant serves what can best be called "sugar and pineapple plantation cuisine" (mainstays of the state's economy in the first half of the 20th century), featuring a wide range of local fish prepared very simply - usually pan-fried, as well as teriyaki everything and pork chops, each served with rice and side dishes. Teshima's is another long-established Japanese-Local favorite in the coffee region.

Really enjoy lurking and reading your blog, by the way, Jason. Thanks.

Another thing you should be sure to do is find yourself a good Shave Ice place. While not uniquely Hawaiian, they've adapted it to their own culture and its a very popular thing to have on a hot day.

http://whatscookingamerica.net/History/ShaveIce.htm

A great blog for finding these sorts of resources is Ono Kine Grindz:

http://onokinegrindz.typepad.com/

I can only speak for Maui eats (been to the island 3 times), so here goes:

Da Kitchen in Kihei. Awesome cheap eats, as local as it gets. Get the pork sandwich or the fried fish sandwich. Amazing!
Aloha Mixed Plate in Lahaina. Another great place for cheap eats, plus it has al fresco dining.
Hali'imaile General Store, excellent when we went there for the first time 4 years ago.
Sansei is good for sushi, 2 locations (Kihei and Kapalua).
I don't know about Roy's in Maui, but the one on Kauai is nothing special (food was oversauced and underwhelming).

Here are the arm-and-a-leg places that may be worth one special night out:
Spago at the Four Seasons in Makena. The salmon "ice cream cones" are, as my boyfriend's brother-in-law would say, "like a party in your mouth" (be sure to visit the spa before dinner for an even greater experience!)
David Paul's in Lahaina. Excellent food, ahi anything is your best bet (ahi tuna is incredibly fresh and delicious in Hawaii).

Have a great time!

Thanks everyone for all your suggestions! I cannot wait to try them out.