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If you live in New York City, there’s no better time than early autumn to play tourist in your own town. Peak vacation season is over — kids are back in school and holiday travelers haven’t arrived yet — but the weather is perfect and the mood is festive.

So I recently took the opportunity to visit one of the city’s newest and most hyped attractions: the observation deck at the top of the David N. Dinkins Municipal Building at 1 Centre St.

At 36 stories, it’s not the tallest observatory — Top of the Rock is 70 stories up, the Empire State Building’s deck is on the 86th floor and One World Trade Center’s observatory reaches the 102nd floor. It’s also not the biggest; only eight visitors can go up at a time, in 15-minute increments.

But for the admission price of $0, Centre 360 at “The Dink” (apologies to the Dinkins family) is the best deal.

It’s also among the most historically significant. Completed in 1914, the Manhattan Municipal Building, as it was then known, was the largest municipal building in the world and remains one of the biggest, according to Yume Kitasei, the commissioner of the Department of Citywide Administrative Services.

“ It was built when we consolidated the city” she said. “All of the boroughs weren’t all one city before … in Brooklyn, they called [the merger] ‘The Great Mistake.’”

To reach the top, visitors have to go through a metal detector, up an elevator to the 25th floor — alongside any other city workers on the way to their offices — and then down a hallway to a separate tiny elevator that reaches the cupola. In other words, this isn’t a ride or an “experience.” It’s just a real place.

Watch our video from the top of The Dink.

“ I’ve been looking at this thing for 50 years just thinking, ‘I wonder what it’s like up there?’” said Q. Mackey, a retired paramedic and one of my tourmates. “ It was virtually impossible to get up here unless you knew a friend or a relative who worked in the building who could escort you up.” He gave it “five stars.”

As it happens, some of those workers were my colleagues — the building was the home of WNYC from the first broadcast in 1924 until our move to Varick Street in 2008. (WNYC, once owned and operated by the city, became an independent public radio station in 1997.)

Katya Rogers, now the executive producer of “On The Media,” fondly remembered the building as having “a general kind of lawlessness,” with city employees, critters and newlyweds all mingling in one structure.

“ Myself, I got married in that building,” she said. “ I was editing. I looked at my watch, I was like, ‘Oh, damn. It’s my slot.’ I said, ‘Anyone want to join me? Anyone want to be my witness?’ And Brooke [Gladstone] was like, ‘Yeah, I’ll come.’ And then we came back to work, and I smoked a cigarette on the roof to celebrate.”

Smoking is no longer permitted on the roof (when I think of it, most stories I’ve heard about the old office involved smoking), but I can confidently report that the romance and the rustic spirit still dwell inside The Dink.

Kitasei issued a challenge to would-be fiancés: “ We’re really hoping that somebody comes up here to propose and then goes down to the marriage court right after.”