What local food in Hawaii should a traveler try before leaving?
Hawaii has so many amazing dishes to try. One found at almost every local style restaurant is loco moco. A hamburger patty on top of rice with a fried egg on the top and smothered with gravy. Lau Lau is a traditional Hawaiian dish of pork, beef wrapped with taro leaves wrapped in ti leaves and steamed until extremely tender. Shaved ice with vanilla ice cream. Ice finely shaved with sweet syrup poured over the ice and a scoop of vanilla ice cream on the bottom. The list is actually endless but this is a good start.
Shave ice for sure. Last time I was home I went to 9 different places in 10 days. The popular ones are Waiola Shave Ice, Shimazu Store. The malasadas are also a great treat from Leonard's Bakery. Plate lunches are all over the place but an old classic is Rainbow Drive-In. I agree with the others that poke is a Hawaiian delicacy. A lot of places do a poke bowl which is the cubed fish over a bed of hot rice.
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Do you have any food allergies or anything that you don't like to eat?
Poi - Honestly avoid the tourist luaus and most of the Hawaiian restaurants in town (and if you do try it at a restaurant ask if can get a sample, most places don't mind because they rather not see people waste it) if this is your first time trying it. Basically there are hundreds of different varieties of taro and the one commonly produced version is grown because of the weight not because it is the best tasting one. That is why so many people get the glue taste notion. My suggestion is that if you want to try good poi you need to either go someone's house, baby luau or a farmers' market. Put it this way one poi from a farmers' market had me wanting to lick the bowl when no one was looking.
Spam - Yes, I will admit that we consume a lot of spam. If you haven't had spam or want to try it in a local way I would suggest either in a spam musubi (rice, piece of spam wrapped with a piece of seaweed, make sure you see the sauce soaked in the rice because dry spam musubis just are not good eats) from some place like 7-11 since they make for a good snack or in saimin which is another local thing you should try in Hawaii (saimin is our version of ramen see https://en.wikipedia.org/wiki/Saimin) which usually has that or luncheon meat inside.
Poke - Basically poke means to cube and in this sense it usually refers to cubed pieces of raw fish (like ahi [ahi is the Hawaiian word for yellowfin tuna], kajiki [blue marlin], etc). Now if anyone tells you that one place has the best of everything take it with a grain of salt because most places specialize or are known for one of two things that they do best. Like I might go one place for Ahi Shoyu (shoyu = soy sauce) and another Ahi Limu (limu = raw seaweed) and another for Spicy Tuna. Also most places also will let you sample a small piece if you ask nicely to help you decide which one you will want to buy.
Cold appetizers like ahi tuna poke and lomi lomi salmon. Main dishes like kalua pork and lau lau (chunks of pork and fish wrapped in taro leaves, amazing), chicken long rice. A side of poi (to explore the unique texture). If possible, get them all 'plate lunch' style. If you're in Oahu, have garlic shrimp from the trucks in the North Shore. Also, loco moco (burger with gravy topped with fried egg), huli huli chicken. Then maladasas and mochi ice cream, and anything with lilikoi (passionfruit) for dessert.
Definitely shave ice with macadamia nut ice cream in the bottom!