A few good places where we ate (all were very good):

The Coffee Shack (early breakfast through late lunch, Monday – Friday)
http://www.frommers.com/destinations/hawaiithebigisland/D34848.html

Nasturtium Café (breakfast through late lunch, Monday – Friday)
http://www.frommers.com/destinations/hawaiithebigisland/D53075.html

Merriman’s (went for lunch, less expensive then, lunch Monday – Friday, dinner daily)
http://www.frommers.com/destinations/hawaiithebigisland/D34868.html

Keei Café (cash only, dinner Tuesday – Saturday)
http://www.frommers.com/destinations/hawaiithebigisland/D34849.html

You have to visit Bubba Gumps..the atmosphere is fun out by the ocean and the food is awesome. It’s a fun place to go, nothing fancy though. This is if you are going to be in the Kona area.
Kona Brewing Co is alright, the food is a little overpriced for it’s taste and there is no view. More a beer tasting hangout and sometimes has live music.
That is all I know for restaurants….I haven’t hit that many myself. Pizza Hut is good! haha It really is though.
Oh yah, Lava Java makes great coffee drinks and is fun to sit outside for a bit.

Yeah, Gump’s is one of our favorites but for Hawaiian style food, I would say that the distinctive local dishes are simple things like spam masubi, which is a large rice roll, wrapped in seaweed with spam in the center. Also, loco moco is rice, hamburger patty, egg and gravy for breakfast. REAL healthy dining. Also, the mix plate lunches are distinctively Hawaiian, where you get fried fish, or teriyaki beef with macaroni salad, green salad and two scoops of rice. Those are the traditional Hawaiian dishes. And don’t forget poi! The grey colored Elmer’s glue that is their starch staple.

For local dishes cheap, to to Kona Mix Plate which is behind Hilo Hatties, downtown.

Aloha

I agree with Gumps. We went late and sat on the lanai overlooking the ocean with torchlight as we ate steamed shrimp and drank mai tais. This is what Hawai’i is about right? There is also a Hard Rock Cafe. For a kick try Lava Rock Cafe in Volcano (near Volcanoes Nat’l Park) we ate there just to say we did. They also have food at the Kona Brewery (and of course you can sample the beers). We did a lot of cooking in our condos just because there was 10 of us and any meal out ran $250-300. I also got coffee at the Bad Ass Coffee Co. so I could get a cup lol.

If you like sushi, Hayashi’s you make the roll is awesome. Its located off of alii drive, next to uncle billys in Kona. You basicly get to choose what you want in your roll (they have all of the normal rolls or local favorites on menu too). Very reasonably priced, not too much of a sit down place there are tables there. Good spot for lunch or to grab and go. open mon – sat 11-6 i beleive.