I agree with the other posters, especially Helena's on School Street. Gotta go with the pipikaula ribs when you're there. A plate lunch is mandatory, and everyone's got their favorites. If you are short on time and can't get in to one of the other aforementioned places, try AW's Pineapple Room in Macy's at Ala Moana. Easier to get into, a little less pricey and a pretty good bang for the buck.
If you have a car and the time, I'd definitely recommend a trip to the North Shore for a trip to the shrimp trucks. If you're in Kahuku, right next to Giovanni's, stop into the old Kahuku Superette, head to the back counter and get the shoyu poke. You won't be sorry.
We only were in Waikiki for one night and while we really wanted to go to Alan Wong's we couldn't make it out there.
Instead we had an incredible meal at Roy's. I was hesitant at first because it's a chain etc. But the meal was AMAZING! Everything was so fresh and full of flavor. A wonderful introduction of things to come on our weeklong vacation. It set the mood perfectly. I can't remember exactly what we had. But the butter fish (I'm pretty sure that's what it's called) that my bf got was some of the best fish I've ever had. And the pinapple upside down cake was so good we almost ordered a 2nd one. :)
Depends what you are asking alexip. If you want the names of the three finest restaurants in Honolulu, I think Hunt's list is right on the mark. Kalihi has some good points as well, although they may not be 4 star restaurants. Nobu's on Beachwalk (or is it lewers?) is arguably the best japanese restaurant around - but pricey. On the other end of the spectrum, what trip to Hawaii is complete without a plate lunch from Rainbow Drive in, Grace's, or Byron's? And somehow you need to have some Malasadas from Leonard's or Champion.
La Mer @ Halekulani
Alan Wong's King St.
Bali by the Sea
I know that you asked for three, but I wanted to make it difficult for you. If I had only one, it would be AW's, at the Chef's Counter.
Alan Wong's Restaurant
1857 S King St Fl 3, Honolulu, HI 96826
Chef Mavro restaurant
1969 South King Street, Honolulu, HI 96826
2199 Kalia Rd, Honolulu, HI 96815
Bali By the Sea
2005 Kalia Rd, Honolulu, HI 96815