When exploring a new island, I scout along the coasts first. While doing so, I'll keep an eye out for visible fish, and mark those spots to go fishing later, especially if I see a tuna.

It's been my experience that the fish-spawning spots do appear to change from time to time. One day a spot might be full of fish, but go back a couple of game-weeks later, and the respawn may have occurred elsewhere.

So... keep looking. As another mentioned, if you don't SEE any fish, you likely won't catch anything.