fresh fish?
I'm not a fish lover, but we always try a selection of local fish to grill while on Kauai.
Several years ago we bought some great Ahi from the Hanalei fish market. Tasted fine, but it was not local, had come from the Phillipines. At other times we have gotten equally good frozen ahi from Cost-U-Less for about $10 less/pound, and once I bought some marked down ahi (something I would usually NEVER do!) from Kojima's in Kapaa that cost only a few dollars. You could tell just by looking at it that it was fresh - it was a small oddly-shaped piece, probably the reason for discount, but was very good! In November, ahi was selling for $14.99/pound, up $2 from a few years ago.
There is a fish market and restaurant in the little shopping center on the left side as you head to the Kilauea Lighthouse. A fish truck on the way to Lihue from the airport sells a local fish that I think is related to mackerel - probably too strong for me. There's a fish market on the mauka side of the Hwy to Lihue form the airport. Used to be a great fish market and deli next to Kojima;s in Kapaa, but they lasted only a few months. Sad.
Probably the only way to get really fresh local fish is to offer to buy from a fisherman, like you can do in Mexico. I see fishing boats close to shore near Pono Kai, but don't know where they sell their catch. Or, you could go on a boat-share with a fishing boat and catch your own!