I've seen many Kauai reports, but most seem to be at least a year old or focused on the North Shore. I just got back from a week in the south with 6 other adults and one 3-year-old, so I have (what I think is) a pretty broad report -- many eaters equals many dishes sampled. In the interest of brevity (and because menus change frequently) I won't often mention specific dishes. This is in the order of meals we ate out, mostly dinners; I've added links to Places entries here, which include Web sites when available. Hope someone finds this helpful. And let me say thank you to the many Chowhounds whose earlier reports I used as the basis for our samplings.
Plantation Gardens (Koloa/Poipu): We stayed at Kiahuna Plantation Resort, so this was our around-the-corner place. I've seen mixed reviews on Chowhound, but our dinner was fantastic. Yes, the service is a little indifferent, but the setting is upscale and handsome and the food inventive, pretty, and worth the high price. Don't try to split meals, though; they're not big enough. Note: We could not get a reservation at the Beach House, the other fancy/delish spot many recommended, which is the one place we didn't visit that I regret.
Tomkats Grille (Koloa): Not my first choice, but surprisingly OK. My sis & BIL loved the fish special dinner, and their potatoes were scrumptious; I was less enamored of the fish taco (huge but with little fish). Pleasant if slightly grungy setting. Great for a large group and for kids, and not too pricey.
Keoki's Paradise (Koloa/Poipu): I'm embarrassed to say we went for lunch (3 of us) and dinner (all 8 of us) on the same day, for convenience. Very pleasant setting, with a sort of inner lagoon, and gracious service at both meals (they're particularly good with kids). The food is not gourmet, but it's not bad; I'd rate it about a 6 or 7 on a scale of 1-10.
Brick Oven Pizza (Kalaheo): We went for lunch. Crust and toppings are good enough, but sauce is out of this world. I think it includes something illegal. We preferred the white crust to wheat, which was too chewy for our tastes. Funky, entertaining decor.
Brennecke's (Poipu): A last-minute dinner option for a big group. We sat right by the windows and watched the sun set over the beach, which was sweet. The many geckos entertained my son. Food was similar to Tomkats/Keoki's, which is to say, not high-end but serviceable, if a bit spendy for the quality.
Olympic Cafe (Kapaa): We went for breakfast, and the raves didn't stop. Impressive, inventive menu; pretty setting; swift service; enormous portions. If you can't make it to the North Shore for brek (i.e., Princeville or Bali Hai), go here.
Poipu Tropical Burgers (Koloa/Poipu): We couldn't make it to Bubba's or Duane's, so we went across the street to the Poipu Shopping Village. The burgers are pretty tasty but overdone (the menu says they cook to "health standards," which translates to no pink whatsoever, so be sure to request rarer if you prefer that). Best kids' menu we saw.
Gaylord's (Lihue): We went for lunch, after a train ride on the adjacent Kilohana Plantation Railway (http://www.kauaiplantationrailway.com..., great for kids!). Again, pretty setting and tasty food, if a bit pricey and not especially Hawaiian (I had a Reuben). Definitely better than Tomkats/Keoki/Brennecke's, tho.
Dondero's (Koloa/Poipu): The best meal we had on the island, and the most expensive by far. They put the 8 of us in our own little room (no view, alas) and treated us like kings, even the 3-year-old. Intricate, astonishing dishes, from an "open-faced" (i.e., made-to-order) seafood lasagna to a Barramundi/asparagus risotto to a strawberry-balsamic gelato. Italian with a local twist, gorgeously plated. Skip the kids' menu, though -- sad for so nice a place.
Hamura Saimin (Lihue): Two of us were in the area, so we chose this over the also-recommended Omoide's Deli in Hanapepe. No atmosphere and brusque service, but a good, hearty lunch for little money. Like udon with different noodles; skip the meat skewers.
Roy's Restaurant (Koloa/Poipu): This was a lovely capper to our week. Not a single miss among our many dishes and drinks (swamp water -- mmm!). Server was a goofball but quick; food was thoughtful and tasty; and the bill, while high, seemed appropriate. Like Dondero's, though, the kids' food is an afterthought.
Other random eats:
Papalani Gelato (Koloa/Poipu): Lappert's still rules and shave ice is most authentic, but this place was a nice change of place. Fresh fruit flavors were quite refreshing.
Puka Dog (Koloa/Poipu): "Puka" means "hole," and here the bun goes all the way around the hotdog. My BIL described it thusly: "They stick all this crap in the hole, like mayo, and then stuff the dog in. Disgusting." I didn't try it, so this is second-hand.
Blossoming Lotus (Kapaa): The main vegan restaurant was closed, so two of us popped in to the juice bar (The Lotus Root) around the corner for an afternoon snack. One coconut tiramisu and two agave limeades later, we were happily refreshed and felt wholesome.
BarAcuda (Hanalei): Heard many good things about it (even as we exited the plane in SF), but just couldn't make it that far north. See this post for a rave: http://chowhound.chow.com/topics/259188.