The critics have never quite called off the search for the great American novel; meanwhile, the hunt goes on for the only slightly less prized great American article. It’s a piece of journalism that captures the spirit and meaning of the republic. Hardboiled but with a soft centre, in the US feature-writing tradition, it might be set in New York, the most American of places.

Indeed, you can still catch staffers at the New Yorker magazine having a crack at it, though they’d never admit it. Their copy might include a zigzagging fire escape, or a genie of steam escaping from a sidewalk, or perhaps a yellow cab hopscotching over potholes. But never all these motifs together! That would risk unfavourable comparison with the cherished chroniclers of the city’s past: EB White, AJ Liebling, Dorothy Parker and others.

But one veteran who has a good chance of joining the pantheon on journalism’s Mount Rushmore is Gay Talese, 93, who has written for the New York Times and Esquire and published 16 books. He remains the man to beat for his classic 1966 piece of reportage rather uninvitingly called Frank Sinatra Has a Cold. Vanity Fair hailed it as “the greatest literary nonfiction story of the 20th century”. It’s included in a terrific new collection of Talese’s stories about New York, A Town Without Time, a title that echoes Sinatra’s serenading of “the city that never sleeps”.

Talese finds Old Blue Eyes pushing 50, extricating himself from a run of ill-advised novelty records and one of his marriages. The writer doesn’t overreach himself, as others might, to explain Sinatra’s quiddity; he does it with some dispatch: Sinatra seemed to be “the embodiment of the fully emancipated male, perhaps the only one in America, the man who can do anything he wants, anything, can do it because he has money, the energy, and no apparent guilt”. Talese’s piece is an eyewitness account from inside the singer’s magnificent entourage. Sinatra has a valet on the payroll as well as a “haberdasher” and a toupee-wrangler who holds his hair in “a tiny satchel”. He is the Sun King, with the rookeries of Versailles replaced by the sunless lounges of Sands casino and Jilly’s saloon in New York.

What impressed Talese’s first readers was his discursive storytelling and insider take. For this he was credited by Tom Wolfe with inventing the New Journalism, a first-person narrative technique later adopted by Norman Mailer, Hunter S Thompson, Joan Didion and Wolfe himself, among others. We have this self-referential formula to thank for the columns that fill the papers now, roaring confessionals about throuples and wild swimming. But today’s readers, and particularly other journalists, will be astonished by the access Talese had, not to mention freedom from nixing PRs.

This was also true of his encounters with politicians and criminals. There’s a grippingly good piece about the kidnapping of mafia don Joe Bonanno. As his leaderless gang lay low to avoid rival goombahs and the feds, it’s as if Talese is filing his pages from one of their apartments. The famous prison cookery scene in Goodfellas, in which Paul Cicero slices garlic to a thou of an inch, has nothing on Talese’s account of these hideouts redolent of sweat and red-sauce meals. “The men had complained that the spaghetti had a metallic taste – they later learned that the cook had knocked his pistol out of his chest holster into the pot.”

You can’t tell where his intrepid research ends and other sources begin, including, perhaps, inspired guesswork. Talese doesn’t show his working: for a New Journalist, this is self-effacing to the point of invisibility. In another story, 1961’s New York Is a City of Things Unnoticed, he puts this civic inattention to rights, noting, among other things, Gotham’s 1,364 messenger boys, 650 doormen in their “heavily festooned” uniforms and the 10 fleapit cinemas that open their doors at 8am. This charming miscellany is the perfect antidote to the listicles of celebrities’ favourite things that clutter newspapers now. It’s a wonderful nonfiction rendering of New York – in fact, a piece of New Journalism to relish at a time when the fourth estate increasingly seems to favour No Journalism instead.

• A Town Without Time: Gay Talese’s New York by Gay Talese is published by Mariner Books Classics (£20). To support the Guardian and Observer order your copy at guardianbookshop.com. Delivery charges may apply