Four days in Los Angeles: How to Love a City Without a Centre

Downtown Los Angeles was written off for decades and is now the most walkable part of the region, which makes it the right place to start before you have hired a car.

Begin at Olvera Street, opposite the railway terminus, which is the oldest surviving corner of the original pueblo founded in 1781 and is now a block of Mexican market stalls and the eighteenth century Avila Adobe. Twenty minutes, and lunch is possible here rather than later.

Walk fifteen minutes southwest to Grand Central Market, trading since 1917 under a neon sign, where forty counters sell everything from handmade tortillas to oysters and there is nowhere to sit unless you are quick. Eat standing up.

Then up the hill on the funicular, which is a hundred metres of railway from 1901 and costs a dollar. At the top are the Broad, the concert hall and the view. The Broad is a contemporary collection given to the city by the man who assembled it, and admission is free, which does not stop the queue; book a timed slot and go straight in.

The concert hall next door is a Frank Gehry in rolled stainless steel, and the garden on the roof is open to the public without a ticket. Finish at the top of City Hall, thirty minutes' walk east, where the observation deck on the 27th floor is free and almost nobody goes.

Hollywood is the thing everyone comes for and the thing everyone finds disappointing, so get it done in the morning and spend the good hours up in the hills instead.

The Walk of Fame is a pavement. Over two thousand five hundred brass stars have been set into it since 1960, the surrounding blocks are souvenir shops and costumed characters who will ask you for money, and it takes forty minutes. The Dolby Theatre at the corner is where the Oscars are held and runs half-hour tours that are better than the exterior suggests.

In the afternoon go up into Griffith Park, which is five times the size of Central Park and mostly undeveloped scrubland with a road through it.

Griffith Observatory is the reason. It was built in the 1930s, it is free, and the terraces on the outside give you the whole basin: downtown in the middle distance, the Pacific beyond it on a clear day, and the sign standing on the ridge behind you. Go up an hour before sunset, look west while the light goes, then turn round and watch the city come on. Parking is a nightmare after four, so take the bus up from the Red line station if you can.

Inside there is a Tesla coil, a Foucault pendulum and a planetarium show that is worth the few dollars it costs.

West today, and the two things at that end are twenty minutes apart and could not be less alike.

The Getty Center sits on a ridge above the motorway and you reach it on a driverless tram from the car park below, which sets the tone. Richard Meier built it out of travertine quarried in Italy and white enamelled metal; the collection runs from illuminated manuscripts to Van Gogh's Irises, and the gardens down the slope are a designed artwork in their own right. Entry is free. Parking is not, and it is cheaper after three.

Give it three hours and go for the buildings and the view as much as the paintings, because on a clear day you can see from the mountains to Catalina.

Then drop down to the coast for the last of the afternoon. Santa Monica Pier is a wooden pier from 1909 with a small amusement park bolted onto the end of it, including a Ferris wheel that runs on solar power and a plaque marking the western end of Route 66. It is unashamedly a tourist attraction and it is also genuinely lovely at sunset with the mountains up the coast turning pink.

Walk south along the beach path afterwards and it takes about forty minutes to reach Venice, which is where the boardwalk and the canals are.

The last morning is one block of Wilshire that happens to hold two entirely different museums, and it is on the way to the airport.

The tar pits are the odder of the two and the more memorable. Asphalt has been seeping out of the ground here for tens of thousands of years, animals walked into it and could not get out, and the result is the richest Ice Age fossil site in the world sitting in a public park with a shopping street on one side. Saber-toothed cats, dire wolves, mammoths, all pulled out of the ground where you are standing, and excavation still going on in front of you.

Next door, the county art museum is the largest in the western United States, spread over several buildings mid-rebuild, with strong Asian, Latin American and Islamic collections. The lamppost installation on the corner is free to walk through and is the most photographed thing in the city that is not the sign.

Then LAX, which is half an hour away on a good day and ninety minutes on a bad one. Leave more time than you think for a Friday afternoon.