The Ultimate Unplugged Vacation? Try This New Zealand Island

“Six hundred people in the Chatham Islands,” continued Mr. Prenderville. “Everyone knows everyone. We all get along pretty well, but there are disputes. Family-type stuff. What do you guys call ‘em, Hatfields and McCoys?” I asked about work. “Not a lot of options,” he said. “It’s pretty much all fishermen and farmers.” Mr. Prenderville works as a commercial diver.

Located 500 miles east of Christchurch, the Chatham Islands are the country’s easternmost inhabited landmass—the first place to see the sun. Of the roughly 10 islands, only two are inhabited, including the main draw, Chatham: 355 hilly square miles, with a dramatic coastline wrapped around cliffs, dunes, beaches and lagoons.

I’d come here on a friend’s advice. While binge-watching the first season of the TV series “Top of the Lake,” I became transfixed with the remote and expansive New Zealand backdrop that seemed the real star of the show. Each episode whacked me over the head with the realization that I desperately needed to unplug and get the hell over to New Zealand as soon as possible. The TV show was set in Otago, on the South Island, but if I really wanted to go remote and dramatic, my friend suggested, I should check out Chatham Island, “part of New Zealand, but totally different—super weird and feral.” I looked into flights—and found only one a week out of Auckland via Air Chathams. My destination seemed sufficiently remote.

I landed at the island’s tiny airport on a blustery evening. A Hotel Chatham staffer greeted me at the only gate for the 30-minute drive to the hotel. Toni Croon, the owner, checked me in. My room was spartan, with sliding glass doors that opened onto Petre Bay, visible only in a stripe of moonlight.

I hit the pub for a counter meal (excellent fried blue cod and chips) and that was when I met Mr. Prenderville. Clad in hiking boots, jeans and flannel shirt, he gave me the lay of the land. I told him I’d be on the islands for a week and asked what I should see and do. “It’s not really about museums or any of that sightseeing stuff,” he said. “Just drive around and have a look. I’ve been living here nearly half a century, and I never get tired of looking.”

Besides providing lodging, food and drink, Hotel Chatham rents cars. One bright morning I rented a mini van that turned out to be Ms. Croon’s personal vehicle, complete with family pics on the dash and a muddy pair of sneakers on the floorboard. I headed west on Port Hutt Road. Passing grassy fields dotted with improbably fluffy sheep, cattle and horses, I marveled at the endemic akeake trees—gnarled, skeletal, bent terrifically sideways from incessant southwesterly winds. It hurt my back just to look at them. I passed a shimmering lake so picturesque it looked fake.

Twenty minutes down the road I drove through a canopy of trees and came to Port Hutt, a tiny fishing village whose centerpiece is the Thomas Carroll, a rusted-out hulk of a shipwreck that ran aground there in 1969 and remains lodged into the rocky shoreline. I parked next to a rusted tractor, just above the water, and went for a walk along the beach and on the grassy area that drops down to the beach. The coastline was littered with what at first looked like driftwood but was in fact sheep, pig and cow bones.

Further along I passed an abandoned fish factory, with a couple of broken down cars parked next to it. One, a Corolla, had vibrant-green vines growing through the interior, with yellow flowers sprouting. The scene reminded me of wabi-sabi, the Japanese concept that beauty lies in imperfection and the natural cycle of growth, decay and death.

If Port Hutt’s landscape possesses a sort of eerie beauty, a trip to the Chatham Islands Museum revealed a history even darker than the scenery. At the museum, in blink-and-you’ll-miss-it downtown Waitangi, I learned that the first settlers, Polynesian tribes, arrived between the 9th and 16th centuries. Known as the Moriori, they lived as hunter-gatherers and fishermen and practiced Nunuku law in which disputes were settled through individual hand-to-hand combat and ceased at the first sight of blood. In 1835, about 900 displaced Maori arrived from New Zealand. Armed with guns, clubs and axes, they proceeded to take over the land, killing, roasting and eating about a third of the roughly 1,600 Morioris. The rest worked as slaves. Back at the hotel, I asked Ms. Croon if she knew where the battles took place. “It wasn’t a battle,” she said. “It was a slaughter. And it happened all over the island.”

Chatham Island doesn’t have cellphone reception and Wi-Fi is spotty. That digital deprivation might unnerve some, but to my mind, it had amazing benefits. People—myself included—weren’t obsessively looking at their screens, or anxiously awaiting a text or call. I was forced to look, to ponder, to make conversation. The entire island felt like a Zen retreat, though a sociable one.

Dining at the Chatham Pub once again—the only place you can get a meal or a drink after 6 p.m.—I met Fiona and Owen, a young married couple from Auckland and avid scuba divers. They were on their third diving trip to Chatham Island. “This place is just bursting with huge crayfish,” said Owen.

As if on cue, Ms. Croon arrived with two plates of big boiled crayfish on a bed of lettuce, tentacles and tail spilling off the edges. Fiona and Owen were drinking a bottle of Sauvignon Blanc from the Otago region (“Top of the Lake” territory), and offered me a glass. Ms. Croon sat down with us, and said that while the fishing and diving areas are bountiful in Chatham Islands, so are the sharks. “Saw one today, but only a little fella,” said Owen.

Ruling out diving—I’m not a fan of swimming with sharks—I spent my days driving the half-dozen or so two-lane roads, stopping at vistas to snap pictures and take notes. One day, I ventured out to a seal colony and after stopping to ask for directions (Ms. Croon drew a map on a cocktail napkin, but it only got me so far), wound up having tea with a farmer, Jim Muirson, and his wife, Sally, in their farmhouse. They showed me pictures of the Chatham Islands from the last 50 years. There was the pub, the shipwreck, Waitangi, those twisted akeake trees. It looked like nothing had changed.

THE LOWDOWN // Unplugging on Chatham Island

Getting There: Air Chathams offers one 90-minute flight a week (more in summer) to and from Auckland, as well as a few weekly flights from Wellington and Christchurch. airchathams.co.nz. The Chatham Islands airport is located 12 miles from Waitangi, the main town on Chatham Island. Most accommodations include transport to and from the airport.

Staying There: The Chatham Islands get no cell reception, though all the hotels listed here offer semi-reliable Wi-Fi. The seaside Hotel Chatham, in Waitangi, has been owned and operated by the Croon family for more than 25 years. From about $90 a night, hotelchatham.co.nz. Located on Chatham Island’s south coast, Awarakau Lodge is the homestead for a 1,300-acre sheep and cattle farm; guests are invited to roam the property. From about $147 a night, awarakau-lodge.nz. Flowerpot Bay Lodge, the sole accommodation on Pitt Island, a 45-boat ride from Chatham Island, offers beachfront rooms and includes three meals a day. From about $180 a night, flowerpotlodge.co.nz

Eating There: Pickings are slim on Chatham Island, but fortunately the restaurant at Hotel Chatham serves delicious fresh seafood, often brought in right at suppertime. Waitangi Road, hotelchatham.co.nz