With its bulbous master bedroom bursting out on stilts, the house at 1350 Ladera Circle is a screaming 1960s architectural exclamation mark. It looks a little like a space station, a little like an old folks' home. And, in its own way, the circular lilypad steps poised above a gushing little stream evoke something of Frank Lloyd Wright's Fallingwater house in Pennsylvania.
I shoot a nosey glance through the glass wall windows of the living room and the sight inside makes me jump out of my skin. Elvis has not left the building. Have you ever knocked on Elvis's door and had him answer?
"Come on in!" he beams. It turns out the guy in the glasses with slicked-back hair is Anthony Alvarez, morning news presenter on NBC's local station in Palm Springs, KMIR Channel 6. Alvarez sashays over to a retro jukebox and puts "The Wonder of You" on as he tells me the story behind the honeymoon home that Elvis shared with Priscilla Presley in 1967 – before he went back to his wild womanising ways of yore. The King (who was the only King told what to do by a Colonel – Tom Parker, his manager) had another house at 845 Chino Canyon Drive where he had the hot tub roofed over so he could indulge himself with princesses and groupies without being snapped in the act. Elvis hated being photographed.
Elvis and Priscilla rented the Ladera Circle house for $2,100 in 1967 after the previous tenant, cheeseburger heiress Marjorie McDonald, moved out. The love-struck couple – who met in Germany when Priscilla was 14 – pulled a scam on the assembled paparazzi when it came to the wedding day on 1 May 1967. Mainly, they got one over on gossip columnist Rona Barrett, who lived further down Ladera Circle and alerted the rest of the press pack to Elvis's presence in Palm Springs. They left all the lights on, explains Alvarez, and escaped over the back lawn, past Marilyn Monroe's gaff, took a jet, and got married in Vegas. If it wasn't for Barrett's curtain-twitching, says Alvarez, Presley would have seen out his years at this house.
Elvis was a loyalist who loved authority. In among the Honeymoon House's kitsch and ephemera; amid the detritus of a man-child who loved peanut butter, guns and girls, is a truly bizarre photo of Elvis receiving an FBI anti-narcotics badge in the Oval Office in 1970 from a lizard-like Richard Nixon.
Palm Springs is, in effect, America preserved in aspic. The pause button has been pressed before Kent State, before Haight-Ashbury, before Zabriskie Point and Punishment Park, before Rodney King. If the American Dream is built on sand then Palm Springs is the apotheosis of that myth; the fantasy of the promised land of plenty out west.
A city shouldn't be built in the Californian desert. A desert city shouldn't boast lush green grass and trees and golf courses and delicate watery mists that keep the restaurant terraces bearable in the kind of heat that would allow you to fry an egg on the pavement. It's unnatural, illogical and undeniably wanton.
That era of America at the height of its imperial power, before the ignomy of Vietnam, is expressed here in a catalogue of buildings of a quality seldom seen outside Midtown Manhattan, all of them concocted in a tiny area. The city was officially incorporated 75 years ago (the anniversary was celebrated in April, on a golf course), at a time when it was already a playground for the rich and famous. Architects were drawn here by the challenge that the desert landscape presented.
There's real refinement among the usual bravado of bulky US architecture. That collection dazzles. There are petrol stations by Albert Frey and villas by Richard Neutra, but Palm Springs's banks really make you stand back. There's pastiche: Victor Gruen Associates' Bank Of America at 588 South Palm Canyon Drive is a crazy hat-doff to Le Corbusier's chapel at Ronchamp. And there's pure optimism in the future demonstrated by E Stewart Williams's clean-lined Santa Fe Federal Savings & Loan Bank from 1960 at 300 Palm Canyon Drive, which is being reopened as the city's new Architecture Museum later this year.
British cities, led by councillors who lack any taste at all, are demolishing their signature Sixties and Seventies buildings. But not in Palm Springs. Everywhere, those magnificent symbols of another time are being re-purposed for the future.
The Saguaro Hotel used to be a run-of-the-mill Holiday Inn – now its balconies are painted in rich primary colours which mesmerise on sunny days (that's almost every day in Palm Springs). Just down the road, The Ace is based on a 1965 Howard Johnson Inn. Both hotels have attracted a new breed of visitor to the desert, with their pool parties and DJ sets. It's all somewhere between Las Vegas and LA's slacker-suburb, Silverlake. These days there are fewer ageing conservatives, more hipsters, more gay visitors.
Just a 40-minute drive away at Indio, you can drink cold beers each spring in what feels like a gigantic open-air branch of Urban Outfitters. Coachella Festival has also, in its rather narcissistic way, rebranded Palm Springs for that mystical "youth market" better than any kind of tourist board could. Earlier this year, the Yeah Yeah Yeahs, Modest Mouse and Beach House entertained the privileged Orange County teens and Hollywood stars such as Robert Pattinson and Alexander Skarsgard on the lush Empire Polo Club fields.
Back in Palm Springs though, the average age of the population is somewhat higher. Pensioners shuffle around – though some of them surprise with their sprightliness, darting around in the heat with a deftness you might not expect. At Armando's in Palm Desert, a drunk group of over- sixties makes bawdy jokes like something out of an episode of Curb Your Enthusiasm. I can barely swallow my fajitas for laughing.
It's also a little Curb at Sherman's Deli, where the staff josh with you between serving up Jewish comfort food classics such as hot pastrami on rye with the kind of pickles you want to write home about. On the wall are signed photos of famous fans of their Reubens – the likes of John Travolta and Barry Manilow.
You suspect there might be a few Manilow LPs lurking in the houses of Palm Springs. After the arrival of such Hollywood legends as Frank Sinatra, whose own home at 1148 East Alejo Road is rectilinear and appealing, a huge building boom in the city attracted OAPs from Illinois, Ohio and New Jersey to the good weather and golf courses.
Robert Alexander and his father, George, were robber barons who doubled the size of Palm Springs by building new houses for the migrants. Robert built 1350 Ladera Circle for his family in 1962 and lived there before Elvis. Both father and son were killed in a mysterious plane crash in 1965.
Death hangs in the air: hospitals and pharmacies and crematoria and churches line the wide boulevards; eagerly awaiting their next customer. Death is a certainty, the only way to live forever is through art: Elvis has his music, the architects have their masterpiece buildings, and at the Palm Springs Museum of Art a wall of names lists the benefactors who've hitched their immortality wagon to the philanthropy horse. Despite appearing like Sixties time capsules, Julius Shulman's photographs of Palm Spring's buildings and David Hockney's homoerotic shots of glamorous young men standing by a Californian swimming pool have a strange permanence which jars with their location in a city built on the sand.
Chris Beanland flew as a guest of Air New Zealand (0800 028 4149; airnewzealand.co.uk), which flies to Heathrow from Los Angeles from £350 return. Upgrade to Skycouch from £169 per couple one way.
Alternatives from Heathrow are available on British Airways (ba.com), Virgin Atlantic (virgin-atlantic.com), United (unitedairlines.co.uk), Delta (delta.com) and American Airlines (americanairlines.co.uk).
Staying and visiting there
The Saguaro Hotel (001 760 323 1711; jdvhotels.com). Doubles start at $158 (£105), room only.
The Ace (001 760 325 9900; acehotel.com/palmsprings). Doubles start at $129 (£86), room only.
Armando's Dakota Bar & Grill (001 760 346 0744).
Sherman's Deli (001 760 325-1199; shermansdeli.com).
Palm Spring's Art Museum (001 760 322 4800; psmuseum.org).