Since we were on an island, we thought it made sense to begin our exploration by water, and so we hired two double kayaks and a guide. We had not kayaked before, and our initial embarkation in the harbor was a bit tipsy, our momentum sending us forth into pilings of the ferry pier, and then some anchored sailboats, and then each other. Finally we made it out of the bay, exploring the inlets of the northwestern tip of the island, hoping to catch a glimpse of porpoises and seals. And although we didn't have any such luck that morning, we did see up close the dramatic shape of the rugged and gently sloped terrain. We paddled ashore at Hakaimango Point, on a spit of tide-washed beach framed by the coastline on one side and huge rock on the other, where we peered into crystalline tide pools filled with periwinkles and baby fish.

On the way back, we had to pause for a few rest breaks, taking a closer look as well at the trophy properties of the island, owned, our guide told us, by some of the wealthiest Kiwis. Waiheke is like all of the world's beautiful islands that way, its prime waterfront homes with starting prices in the millions. But this is still New Zealand, which means that even during the summer high season the island feels as crowded as Martha's Vineyard in October, and though the wineries and their restaurants tend to be tony, high-design affairs, the underlying vibe is distinctly agrarian, low-key, and modest, if with a hipster gloss. Nobody is in too much of a hurry, even in "downtown" Oneroa, where the galleries and handicraft shops and cafés are lively but not in the least hectic. It was not much of a surprise to learn that Waiheke was a notorious hippie hangout in the sixties and seventies, a refuge of pot farmers and burnouts and surfers who settled among the long-residing dairy and sheep farmers and fishermen, counterculture types who starting in the mid-eighties were joined by (and in some cases morphed into) craftspeople and artists, olive and grape producers.

After we left Waiheke on the ferry, during the long, lovely drive down the North Island on our way to Hawke's Bay, I kept thinking of the island's first Polynesians, sailing thousands of miles over open ocean in their narrow longboats, or the European (and handful of Asian) settlers of the eighteenth and nineteenth centuries—how you'd have to be amazingly self-sufficient and resourceful to make it in this land, how you'd have to be possessed of certain necessary attributes to survive and then prosper: a belief in one's labors; an alertness to constant change; an acceptance of factors beyond one's control; and, perhaps above all, patience. Maybe this very landscape promotes patience, encourages you to open your eyes and let it all be: There are huge plots of pastureland and produce and tree farms on either side of Route 1, the immense plateau shouldered in the far distance by the moss- and sand-hued Kaweka Mountains etched sharply against the bolt-blue sky. Driving in New Zealand is a strange, almost anachronistic joy, to move in comfort and at a modern speed in a tableau that in many moments, with no other cars in sight, appears pre–Industrial Age. Route 1 itself, for example, is a major highway and yet just a divided two-lane road, and my daughters enjoyed seeing all the animals along the way, the dairy cows and horses and emus and alpacas and wild rabbits, and of course the sheep. You drive always with sheep. People talk of sheep in New Zealand, and although I still don't know much about them, I will say you get to know something of their variety while driving the country: their sated, sleepy-sad expressions, the white-faced ones and black-faced ones and the stout older mutton and the sweet-kneed lamb, the just-sheared and unsheared, and those grazing on the impossibly steep side of a craggy hill so far in the distance that they look like cottony white ticks, if there were such a thing, so very hungry and very still.