Hurunui Mouth is accessed off the main highway along Hurunui Mouth Rd. There is a Scenic Drive sign 2/3 of the way along the road (to Gore Bay), but continue on. At first sight, there is no particular reason to go to Hurunui Mouth. But it is pretty enough, you can stay at a campsite beyond the hamlet, fish, and get a boat in and out on the water. If you cross the river near the campground, you will access a pretty wild strip of remote beach with no official name.
You can’t see it from the riverside by the campground, but the river spreads out into a large lagoon between the beach and the cliff to the north, before eventually entering the ocean.