Deirdre has arranged for one to meet us at various times, but we're always stood up. It's no surprise because she has also told us they are extremely secretive about their spots.
We give up waiting and head down to the beach and its sand-dune wastelands, the landscape bathed in sepia tones. It feels like we're walking through one of the faded photographs back at the wharf store.
A few whitebaiters in waders are out in the rushing river flow, but our children, aged five and eight, are already running through the dunes, so we chase them before they're lost in the desert-like surrounds.
We come across strips of pumice stones, fields filled with old couches and large areas covered in broken shells. As we get deeper into the dunes, we realise we're all lost. It's a nice feeling of freedom having just the crashing sound of surf waves as our guide.
We struggle with our parental need to finish the walk and the kids' desire to live in the moment and run up and down every dune. When I do hurry them up, my five-year-old quite rightly points out: "I thought you said we were coming here to have fun."
With no coffee shops, no telephone reception and no alcohol for 30km, we follow her lead and slow down, which is what Deirdre tells me is the region's drawcard.
We eventually make it back to camp only to head out again to a working dairy farm for a Close Encounters Farm Experience tour.
There are 140 cows at the farm, run by Rita van Vught and her husband David. A couple of cows have just given birth so we get to watch the calves' Bambi-like first steps.
The farm is home to too many animals to mention — it's overwhelming thinking of Rita looking after her children, her cows, her homestead and her huge variety of animals. As if that wasn't enough, she opened the farm for tours a couple of years' ago and says senior citizens are just as keen as pre-schoolers to come for a visit.
Some of the animals we meet on the tour include a cockatoo who waves and wiggles down a tree branch to say hello; Blinkie the Flemish giant bunny and her dwarf bunny companion, Larry the cockatoo, who nibbles on my shoelaces; guinea pigs; timid turtles whose shells peel because they're always growing; and emus known as Louis and Lucy.
We also meet golden pheasant bachelors and a Lady Amherst pheasant from China. They're delicately decorated like colourful hand-painted porcelain. We also meet the kune kune pig, a less attractive creature, whose hair can be made into a hairbrush.
My favourite birds, the Madagascan love birds, are in a cage nearby. They breed for life and sit in pairs preening each other's matching feathers.
There are also wild peacocks — one takes a shine to us and displays its feathers, creating a vibrating sound. The peacocks sleep in the big trees at the top of the farm's paddock (climbing up branch by branch) and come down the hill to visit. We're shown llamas and alpacas, as well as goats (apparently they're very brainy) and pretty Scottish highland cows (who don't have top teeth). There are also Jerusalem donkeys with cross markings on their backs, and the kids get a quick ride on one of them. Then they feed the lambs with little milk bottles, while a small dog taunts the rams.
We're then bundled on the back of a tractor, sitting on hay bales, and head out to meet the curious cows.
Then it's off to the milking shed where it takes the family two hours to milk their cows, twice a day. The kids are given pony rides on horses that have manes plaited and adorned with ribbons.
Back at the holiday park, we finally come close to the white-bait, choosing whitebait fritter burgers from a tiny burger van. It's the closest we got to the famous local fish, but it was well worth the wait.
River road-trip
Stay at: Port Waikato Holiday Park. It's so close to Auckland that I'm told families often holiday here but head back for appointments back home during their holidays.
Visit: Farm Encounters. Bookings essential and by appointment only.
Travel in a: Britz campervan — they even have a "swap and share pantry" if you're game to try hardly worn Jandals or tins of beans left behind by fellow campers.
Danielle Wright was a guest of Britz and Port Waikato Holiday Park.
