Shannen Doherty waves to me and Johnny Depp tried to buy my house

When we want to titillate visitors with a taste of Hollywood, we take them down the hill to the Bar Marmont on Sunset Boulevard.

From the outside, it looks like a low wooden shack with peeling grey paint; the name scrawled carelessly on the fence at the front. Inside, it is a small room with closely-packed restaurant tables, comfortable cane arm chairs in an alcove and myriad butterflies pinned to the ceiling. They serve exquisitely expensive margaritas and recommend a particularly smoky brand of tequila.

The bar is close by the Chateau Marmont hotel, a local pied-a-terre for film and music stars, cultivating a slightly shabby, off-beat feel.

The Bar Marmont's opening was marked by a rare honour - a story in the New Yorker magazine's "Talk of the Town" section. This month's Travel and Leisure magazine confirmed it is "the" bar in Los Angeles. If you want to mingle with the stars after dark, you are virtually guaranteed a sighting.

We go there early, before the crush and the queue of cars at the valet parking. The first time, a starlet from the film The Mask was doing a photo-shoot, twisting and wriggling at the bar for the photographer while the staff looked on approvingly.

I once took the entertainment correspondent of The Scotsman, who had just been to the Academy Awards for Braveheart, wearing a kilt. In a flash of brilliance, he spotted one of the Monkees in the corner. On the way out, we nearly bumped into Christopher Walken.

In Hollywood, there is the A list, and then there is the rest of us looking on. Occasionally, people swap sighting stories. Unfortunately, neither I nor my wife are very good at celebrities. Either we don't recognise them in time, or we don't know who they are. In The Source restaurant, a cheery place just along from the Chateau, my wife saw a man who looked like a slightly bronzed, pudgy hairdresser. It was Fabio, the cover model of countless paperback romances.

Johnny Depp once offered to buy the house we now rent, along with several others on the same street. It overlooks his three-acre estate and a 20- room turreted faux chateau, a pre-war building in the same style as the Chateau Marmont.

He is a stickler for privacy. Having failed to buy the surrounding homes, ostensibly for some of his relatives, he built an eight foot high fence of welded industrial-grade steel around the estate, with thick green bushes to obscure the view. Neighbours complained and his managers had to take a foot or two off in places.

Shannen Doherty waved to me cheerily last week. I was plodding up the hill, unkempt, sweaty, pushing our daughter's stroller. Shannen came swooshing down at the wheel of her heavy black Mercedes, her car phone pressed to her ear.

Shannen is an absolutely certified star. She lives near us in the Hollywood hills, and has such a reputation that at the mere mention of her, people's faces sour as if they've bitten on a lemon.

So far, she hasn't lived up to it. She doesn't even play loud music, though her boyfriend's dog trapped us inside our house one day, growling nastily. We babysat her Alsatian once, when the dog taxi dropped it off early. Shannen became famous as a teen vixen in Beverly Hills 90210, so I wonder if her reputation has rubbed off on real life.

On Saturdays, the tourists come past, because Shannen is on the front page of the maps to the stars' homes they sell down on Sunset.

Her friends all drive expensive black cars, Jeeps and Mercs, and they slide past the kitchen window after supper while we're washing up - on the way to the Bar Marmont, presumably, or some other celebrity magnet.