We spent a week on the North Shore in Kauai at the end of Feb/beginning of March. It's much more mellow and not particularly a food destination (say compared to Poipu), but there's plenty to enjoy. Some highlights:
Hamura Saimin -- Ok, it's in Lihue, not on the North Shore. We ate here 3x, yes 3...after we landed, once during the week and we picked up to-go as we headed for the airport to come home. It's an institution. My bowl of choice was the Special Saimin (won ton, ham, hard boiled egg, bok choy) and you've gotta get BBQ chicken or beef skewers.
Pat's Taqueria (Hanalei; Black Pot Beach Park): Taco Truck + surfers = delicious Mexican chow. The carne asada taco is the standout. Kalua Pork is good, too. The tacos are crispy taqueria style (versus hard shell). Fillings are generous.
Hanalei Pizza (Hanalei) -- Solid pizza, super friendly service. We had the Veg-Head + pepperoni and took it to-go. We enjoyed some BYO wine while waited (they were nice enough to provide real glasses) and even offered us some appetizers...a pizza that had gotten a little overdone by their standards, but was actually just extra crunchy, not burnt.
Hanalei Farmers Market (Saturdays, opens at 9:30 a.m.) -- Get there when it opens (or even a little before). Frequented by both locals & tourists, it's a great source for strawberry papayas, mangoes, rambutans, avocados, salad greens, local citrus. The other half of the market is crafts and prepared foods. Try Sal's Salsa & the Kauai Kunana Dairy feta.
Foodland's Char Siu Chicken Legs -- It's the grocery store in Princeville, but if you've got a kitchen where you're staying, pick up these pre-marinated drumsticks and bake 'em up in the oven. You probably can't get them at home -- delicious.
We also tried Postcards and Bar Acuda in Hanalei. Postcards is mostly a fish place, and I'm not much of a fish eater, but the husband liked it. They do have a few non-fish items and some delicious taro fritters. Their first come/first serve seating can be a little kooky, so go a little before they open for dinner and put your name in or line up and be prepared for a crowd.
Bar Acuda, I'd call modern American tapas. They feature some local ingredients and it's perfectly tasty, just nothing really unique.
In Lihue, we tried twice to catch the malasada lady in front of Kmart, but never timed it right. Opening time is approximate, but we'll definitely we trying to catch her on our next trip.