Los Angeles, California: The hippest hotel in West Hollywood has to be Sunset Tower

Over breakfast I read that Iggy Pop used to fairly regularly dive from his apartment window, several floors above me, into the pool below. He obviously survived, but often an ambulance had to be called to attend to his injuries. The Godfather of Punk, who has always had a penchant for baring his chest – even now at age 72 – has never had a body image problem.

As I look out over the pool from my possie on the Sunset Tower Hotel terrace, I think that you would have to be comfortable in your own skin to slip out of the hotel's monogrammed bathrobe and enter the pool, even by diving from its edge or stepping in via the marble stairs, in full view of diners.

Several guests are eating breakfast nearby, stretching out the morning meal into brunch, reading, tapping away on laptops and talking into mobile phones. I don't spy any celebrities from behind my sunglasses, even though this beautiful art deco hotel in West Hollywood, once an apartment block, is in the thick of things on Sunset Boulevard and known to be a place for a brush with fame.

I'm glad it's a crisp May morning, too cool for a swim and with no need to disrobe; I add another dollop of strawberry jam to my croissant, sit back and take in the view past the pool to the gleaming high-rise of downtown Los Angeles.

Sunset Tower Hotel is a stylish address on the famous Sunset Strip, a 2.6 kilometre stretch of Sunset Boulevard and the epicentre of LA's night life. When I exit the building and turn left, it's a mere stroll to haunts I've heard so much about. There's the Viper Room, once co-owned by Johnny Depp and where actor River Phoenix died in 1993; Whisky a Go Go, the Rainbow Bar & Grill – well-known as the hangout of heavy metal rockers – and the Roxy Theatre, where The Rocky Horror Show premiered in 1974.

But alas, there's no evidence of 77 Sunset Strip, the 1960s TV crime show I watched as a kid. In fact, number 77 doesn't exist on the Strip, but there is a plaque on the pavement denoting where a film set once stood. I blithely walk over it.

Sunset Boulevard is a wide, busy thoroughfare, more Parramatta Road than the tree-lined streets of nearby Beverly Hills. However, the sight of so many famous celeb and rock star haunts, albeit seen under the glare of the midday sun, does make up for its harshness. I pop into Mel's Drive-In, a diner that occupies a listed Googie building, a style of architecture marked by a space-age up-swept roofs. Mel's looks like it came straight from the Happy Days set, and serves classic Americana: hash browns, eggs-over-easy and brewed coffee. I order the clam chowder, which is delivered by an Aussie waitress.

Back at my digs I wallow in the understated elegance of my 12th floor room. From the east window I can see down to the Chateau Marmont, another star hangout and forever remembered as the place where John Belushi died from a drug overdose in 1982. From my eyrie I can clearly see why the area is called the Hollywood Hills. My room is a study in soft pinks. I love the two-toned cream and pink walls, broken by the chocolate leather of the bed headboard and desk. Diaphanous drapes have a blush of pink, as do the fluted silk standard lampshades and the velvet cushions placed here and there.

My embossed robe ($US95, available at the front desk) is in a matching tone. The room seems to whisper Marilyn Monroe. She lived at the Sunset Tower when it was an apartment building, as did other stars of the Golden Age: Greta Garbo, Joan Crawford, Errol Flynn and John Wayne, who apparently kept a cow on his penthouse balcony because he liked fresh milk with his coffee. The bathroom is charming. I love the gold wallpaper with its stylised drawings of the hotel, classic LA palm trees and glamorous people. Everything is embossed: the compendium, the full-sized bottles of shampoo and conditioner, even the pouch for slippers. A chocolate model of the hotel is delivered to my room on an embossed plate. They do make it rather tempting to nick something – surely the pen, stationery and a tiny bottle of body lotion won't be missed.