Mama's Fish House-
On the North Shore, right on the ocean.. The views are unbelievable and the food is to die for...Kind of pricey, but if you go during lunch, you get awesome food at less price!
Hawaii -- anywhere. Order fish. Ask if it is fresh, usually it is, but in Honolulu we found some restaurants that sell frozen Mahi-Mahi, a shame when such fabulous fresh fish is available. What to order? Ahi-tuna, ono ( moonfish), mahi-mahi (dolphin -- not the warm-blooded flipper type) opah, and many other Hawaiian fish. In Honolulu Waikiki, we had great fish at Dukes ( but very noisy with surfers), Chucks ( next door), and Hatsuhana ( Japanese) and excellent Chinese food at the Golden Dragon, both of which are in the Hilton Hawaiian Village. We also stumbled onto a wonderful all-you-can eat buffet on the top floor of the Ala Moana shopping center. I can't remember the name but it was entirely local Hawaiian food for $20.
In Lahaina, Maui, Hawaii, we had excellent fresh fish at Kimo's, the Fish House, and Cool Cats. These are pricey -- in my books -- but no where near as pricey at the Mama's Fish House mentioned above. I do believe the fish at Mama's is superb, but we decided not to afford it. At Da Kitchen in Kahului, my husband ordered Moi (mullet) almost at the insistance of the very friendly staff. They said Hawaiians love it and it is seasonal and if he ordered it at Mama's he would pay $40 for it. So he ordered it for $22 and loved it. It was very fresh. No doubt at Mama's it would have had a fancier ambiance and perhaps preparation method, but my husband inhaled it.
There is a great book available in Hawaii called The Puka Guide by Dela Cruz and Chai, which I highly recommend. Pukas are holes. In this case hole-in-the-wall restaurants with great food. I can highly recommend on Maui, Da Kitchen in Kahului, Aloha Mixed Plates, in Lahaina and Honokowai Okazuya. All of them have fresh mahi and the first two had great Kalbe ribs. They do not have much atmosphere and some even use paper plates, but the food is wonderful and far less expensive than the places operated for tourists. There is a book on eating out just on Oahu as well. We didn't buy it but it looked very promising. Most bookstores in Oahu have it. The Puka Guide covers all the islands.
Most people take in a luau in Hawaii. The best one I have seen is The Old Lahaina Luau behind Safeway in Lahaina. The address sounds inelegant but it is on the beach in a very beautiful spot. It is about $90, but it gives you a sample of a large number of Hawaiian dishes in a generous buffet, free open bar, and really authentic hula. We really loved it and it is highly recommended by Lonely Planet and our travel agent. I have been to other luaus and have not found them to be any where near as well done as this one. You absolutely must have reservations, but when we found them full for a week we asked to be put on a wait list and eventually got in. Our table was excellent.