A few suggestions:

-On the main drag on the south side of the island, there’s Shrimp Station (great spot for lunch). Outdoor seating on lawn furniture. You’re also walking distance to quite possibly the best shave ice you will ever eat (the one off the main highway).
-You must have a Puka Dog (in Poipu). It’s in a strip centre (there’s a Roy’s in the plaza).
-Brenneke’s (at Brenneke Beach) is a great dive bar/lunch spot…right on the beach.
-There’s a Lappert’s Ice cream in Koloa next to a better-than-it-should-be pizza place.
-If you want the romantic dinner, there’s a place on Lawai Road in Koloa that has sunset dining (I was there for a work conference for a week over the summer and stayed over an extra week); food is quite decent, views are outstanding (we had a dinner outing there; it’s mostly couples).
-You could also eat at Roy’s (in Poipu), but again…it is a chain (upscale chain, but still). Their seafood is generally pretty good.
-There’s a Vietnamese/chinese place close to the Marriott resort; it’s a madhouse, but their food is excellent. Do not be scared by the somewhat rough looking exterior/interior or the clientele.
-There’s several decent places along the main road not too far from the Hilton resort. Mostly locals frequent them.
-There’s a diner over there (near the Marriott resort) that is also quite good.

If there’s a Chapters (maybe Borders in the US?) nearby, I’d strongly suggest getting a copy of “Kauai Revealed”; it’s written by locals and their recommendations on food were almost always bang-on.

Suggestion- ask a local what’s good. If you hear a place mentioned more than once…check it out.

Happy traveling!