You can smell something sweet and seductive as you stroll around Jackson Hole, Wyoming, and it’s not just the crispy clean, mountain high, pollution low air you’re sniffing. It’s money, one of the sweetest smells of all. And loads of it.

It may not be as glamorous as Aspen, Colorado, or as infamous as New York and Beverly Hills, but the Teton County area of Wyoming that contains the skiing and cowboy town of Jackson (calling it a hole seems unkind) is home, or perhaps second or third home, to more rich people than any other place in the US.

And it’s not just the celebrities – including Harrison Ford, Sandra Bullock, Brad Pitt, Pippa Middleton, Tiger Woods, Uma Thurman, Matthew McConaughey and, most recently, Kanye and Kim – who roll into this vertiginous valley to build or buy “log cabins” in the hills, it’s the heavy-heavy-hitters of tech industry, too.

Think Wal-Mart heiress Christy Walton, who’s worth $7.1 billion on her own, or former Vice President Dick Cheney, or Bill Gates, who bought a ranch formerly owned by William ‘Buffalo Bill’ Cody, for $US9m.

The result of all that wealth is that, according to a report by America’s Economic Policy Institute, the average annual income of the wealthiest one per cent of residents in Teton County is a staggering $28,163,786. Making that figure even more incredible is the fact that in the county that comes second, New York, the top one per cent average “just” $8,143,415.

As one of the report’s authors, Mark Price, puts it, Jackson Hole seems to be the answer to the question: “If you were a billionaire, where would you want to live in the United States?”

As soon as you step out of your plane at the local airport – which becomes so overcrowded with private jets at busy times of the year that they have to park them on the grass – you can see at least part of the appeal.

The scenery here in the once-wilds of Wyoming really is on an epic scale. The Snake River (offering some of the best fly fishing in the world, apparently) winds picturesquely through the Hole of Jackson (the “Hole” is what they call the valley, but it’s become attached to the town) with the towering Tetons on one side and a matching mountain range, the Gros Ventres, on the other.

Come in autumn, as we foolishly did – thus missing out on the incredible skiing the area is arguably best known for – and you’ll see acres of leaves turning from green to almost luminous yellow, seemingly before your eyes.

It’s impossible to describe the width and breadth of the beauty here, but the best story that encompasses it is that when we sent the Voyager II space craft into the depths of our galaxy, back in the 1970s, scientists included an Ansel Adams photo of Jackson Hole as a slightly exaggerated version of what life on Earth looks like, in case any aliens were interested in buying real estate.

Despite being so exceptional, the landscape also feels somehow familiar, and that’s because it’s been in so many great films. Genuine cowboy country that it is – there’s a rodeo ring right there in town and the Million Dollar Cowboy Bar is genuinely filled with them most nights – this is where many famous westerns were shot, from John Wayne’s first film, The Big Trail, in 1930, all the way through Shane, The Outlaw Josey Wales, Dances With Wolves, Django Unchained and even Brokeback Mountain.

Sci-fi fans would more likely recognise the big-sky country from the classic Close Encounters of the Third Kind, or the first ever Star Trek film.

After a couple of days here with some colleagues, being pampered with an inch of our lives at the suitably superlative Amangani resort, just outside town (Justin Timberlake stays there when he’s skiing), some doubters were heard to express the thought that, while the area is lovely, it does feel a bit remote, and “if I was a billionaire, I’d want to live somewhere a bit more exciting”.

But what Wyoming offers that places like New York and LA can’t is privacy, something that’s far more prized by the rich and famous than the rest of us. Your money buys a lot of space around your private ranch here, and when you roll into town for groceries – as Harrison Ford did, in an Aston Martin, one day while we were there – the easy-going, unaffected locals just leave you to it. (Sadly Kanye still got insta-papped by visiting tourists while he was in town with his photo-loving wife.)

It is, in short, a wonderful place to get away from it all, and the more money you’ve got, the nicer it is.

(Lead image: Jackson Hole Mountain Resort Photo: Facebook)