I am lying on the sand at Sydney’s Cobblers beach in the early 00s, half-asleep in the sun. A friend hands me her Discman and says, “Listen to this band. The guy keeps singing about streetlights and girls, but in a good way. And apparently everything is about New York.”

The CD was Interpol’s Turn on The Bright Lights, a post-punk album throbbing with inspiration from Joy Division and the Psychedelic Furs. From the opening of reverb-soaked guitars on Untitled, I was transported to a world far from my sunny outlook – the New York night. I had passed through the looking glass into a noirish atmosphere of alienation and ennui. But among the bleak textures there was also a sense of romance, conjured by the lush production and Paul Banks’s haunting vocal style. I was able to form images of New York that belonged more to a mythology of the city than any real experience.

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In songs like Stella Was a Diver and She Was Always Down, with its dreamy character portrait and driving bass line, Interpol echoed what F Scott Fitzgerald and Patti Smith had already suggested to me about New York. It is a place of quick and restless adventure, where the blinkers of taxis hold the restless eye in a pause; where it is possible to follow poor lovers along 13th street and watch them disappear under eaves into unknown rooms; where conversations take place until dawn, wild conversations about how all of the world’s art belongs to the New York night, where every creative act can somehow be understood beneath the enchanted streets.

If that sounds a little much, maybe Interpol aren’t for you. Their vision of New York asks you to suspend knowledge of the wholesale destruction and clinical real estate development of what were once artistic enclaves. Today, in the Trump era, aspiring musicians are unlikely to encounter the likes of Lou Reed or Klaus Nomi in a downtown bar. Instead they’ll have to shield themselves from trust fund kids pretending not to flash their Patek Philippes and Wall Street types telling incomprehensible jokes about quaaludes.

In the post-9/11 world, the song NYC expressed the detachment and vulnerability of trying to navigate the new century, one in which suicide bombers could murder thousands in a city that housed the United Nations, and the growth of digital media meant the reconfiguring of relationships. I listened to it on repeat, on the beach at 3am, and then later sprawled out drunk under blue gums in Gundagai, far from New York itself. When Banks sings, “I’m sick of spending these lonely nights / Training myself not to care / The subway is a porno,” it felt like a window onto that city’s subterranean soul. Underground, the city is stripped of its sheen, naked and dirty. The song captures the particular melancholy that accompanies being lost among millions of other restless lives.

Facebook Twitter Pinterest Interpol are currently playing in Australia. Photograph: Jamie James Medina

Over the last 16 years, Interpol have released five other albums, including the recent Marauder, which they are currently touring in Australia. Their songs have continued to evoke images and moods of New York City, some more explicit than others. On Next Exit, the opener on Antics, an eerie church organ swells to the point where the drums kick in, as if banging on a grand old door: “We’re goin’ to the city / Goin’ track this shit around / And make this place a heart / To be a part of again.” The melodies on No I in Threesome and Pace is the Trick, both from Our Love To Admire, capture storied midnights of whisky and valium, where figures seem to stumble from Central Park onto the Upper West Side to catch a glimpse of neon. On Same Town, New Story, from El Pintor, Banks sings that it “Feels like the whole world’s coming down on me / Wide eyed, venture so slowly.”

In a 2014 interview, the band was asked about their relationship to New York in the 21st century, with its glassy condominiums and cookie-cutter architecture. Drummer Sam Fogarino said that although the city had changed dramatically, “there’s still something about New York. As soon you step on the sidewalk, you’re fucking in New York. It’s still pure. Everywhere you look, everywhere you walk … It’s still the best fucking city in the world, no matter what phase it’s going through.”

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Even at a vast distance, covered in a mask of sea-spray, Interpol allow me to inhabit the world of old New York, as if I was behind the camera with David Wojnarowicz in the late 1970s, or shooting hoops with Jim Carroll on the Lower East Side. Listening to their cinematic hooks, I become an anonymous figure in a great dark metropolis.

• Interpol are playing in Melbourne on Friday 4 January at Sydney on Saturday 5 January