The closest thing you are going to find to fine dining on the north shore is at the Turtle Bay. The food is much above average hotel food, but calling it fine dining would be pushing it. The Palm Terrace, 21 degrees north, and Ola have all gotten decent or better reviews here in chowhound.
The north shore is not about fine dining, more about great grinz as we like to call them. Jameson's has an incredible view, as does Haleiwa Joes. I have always had good to very good food at Jameson's, some people have been less fortunate, or are pickier than I am. Skip the fine dining and go for the local stuff. Shrimp trucks, Kua Aina for Burgers, and the afore mentioned Jameson's and Haleiwa Joes. Pizza Bob's gets good to moderate reviews as well.
Remember, you are in an isolated rural area, 30 miles from the city. This is not a resort district, but a struggling agricultural area with spectacular natural beauty. If you must have a real fine dining meal, take the 45 minute to an hour drive through Haleiwa and Wahiawa, and back to Honolulu.
if you want want an excellent steak, go to foodland and buy a good cut, a couple of pounds of assorted poke, a bag of poi, and some good beer. Then go find some locals bbqing on the beach and offer to share. (I'm only half kidding.)
There are no great steaks on the North Shore. I'll second Hale'iwa Eats, it's not fancy but the food is good. This area has little to no find dining. I've not been to Jameson's because it gets panned for its food, but the setting is the closest to fine dining as you're going to find in the area.
I'm jealous as the North Shore is one of my favorite vacation spots and I was married at Turtle Bay 2 years ago. The breakfast buffet at Turtle Bay with the coconut/macadamia nut syrup on anything is fantastic!
Matsumoto's Shaved Ice is a must dessert/snack.
Jameson's in Haleiwa is great for dinner..It is island nice...seafood...overlooks the ocean and has great sunset views. Been going for at least 14 years and it hasn't let me down.
Enjoy and please report back!