ONE PUB, ONE takeaway shop, one general store,” said Floyd Prenderville, a solidly built man with a goatee, describing New Zealand’s Chatham Islands, where he’s spent the bulk of his 47 years. We were squeezed into the Hotel Chatham pub, in the main island’s main town of Waitangi, and it was Ladies’ Darts Night. Tattooed men huddled over pints at the bar. Elderly couples in wool coats played slot machines. A coterie of women in jeans and rubber boots threw darts and high-fived.

“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.