A major exhibition of Van Gogh's work and letters has just opened at the Royal Academy in London. But a trip to Amsterdam might offer another clue as to what inspired the artist's familiar wonky lines

In Amsterdam's Van Gogh Museum the curator's note alongside the famous Potato Eaters suggests the artist has cocked-up his perspective – technically we should not be able to see the back of the chair on the left of the painting. But we do.

Driving in from the airport it seems that much the same could be said of central Amsterdam. No two adjoining houses seem to share the same vertical line, the horizontals splay off at random, lampposts look wobbly, and the only thing that seems to keep entire rows of canalside buildings standing is each other – like staggering drunks propped up by their own equal and opposite improbability.

Amsterdam is hand drawn by a child. And though Vincent only spent a single year here – 1877 to 1878 – it seems entirely plausible to me that his artistic habits were formed by the wonky lines of the city. Though he didn't start painting for another three years, his idea of perspective could have germinated here. Stay with me. If my new instant theory stands up, could it be that Vincent was an accomplished draftsman from the off, and it is Amsterdam we should thank/blame for the dizzy perspectives in later works, such as The Bedroom?

My bedroom for the duration is in one of my favourite hotels, The Pulitzer. It is probably the wonkiest hotel in this wonky city. From the outside it is almost invisible, betraying its existence only through a modest lobby on Prinsengracht. The rest of its 230-odd rooms are concealed in a maze of 25 adjoining houses dating from the 17th and 18th centuries. They occupy the entire block between Prinsengracht and Keizersgracht. No two rooms are the same; internally they are connected by a warren of passages that twist, turn and jump levels like a springbok on speed. There is no over-arching design. The hotel simply rambles; enclosed corridors cut across the internal gardens and the function room, the gym, the bar and the restaurant all seem to pop up without any rationale. The Pulitzer feels more like an organism than architecture. It is intimate, even eccentric, wearing its corporate position within the giant Starwood Hotels group very lightly.

From my window I can see the canal is frozen and the world out there has the austere palette of a winter scene by Hendrick Avercamp – minus the skaters, though, because the ice is too thin. Prinsengracht is its own little world within a city – with an eclectic range of shops. Check out the absinthe specialists (Quinta, 4 Nieuwe Leliestraat), cosy "brown" cafes (Het Molenpad, Prinsengracht 653), stylish restaurants (Envy, Prinsengracht 381) and renowned landmarks. Lazy weekenders could easily nominate this one canal as a destination in itself.

Two blocks from the hotel, just past the monumental Westerkerk, which has the highest tower in Amsterdam, a long queue straggles around the corner from an unremarkable building. The wind has a biting edge but that doesn't seem to impact on the crowd. They are waiting to get in to the Anne Frank House. I last visited it more than 20 years ago. The Anne Frank experience is now layered and mediated by the modern museum that has been built in the two neighbouring buildings. The house attracts a million visitors a year and it is inevitable, given the demand, that the visit is more managed. Anne's story is told simply, but a range of multi-media techniques is deployed to shepherd the endless flow of traffic through the limited space.

The annexe itself, where the family hid, remains bare and utterly crushing. The chatter of the throng, including many children, diminishes as the tour progresses. In the room immediately after the annexe, where the fate of the inhabitants in various Nazi death camps is spelled out (of the eight inhabitants only Otto Frank, Anne's father, survived), an eerie quiet descends on visitors. Downstairs, in the foyer, an improvised shrine to Miep Gies, one of the small group who helped the Frank family in hiding, has been set up. She died just this month, aged 100 – one of the last living links with Anne Frank has been severed.

Annelies Weisselberger, a museum volunteer whose own parents were also sent to concentration camps, kindly takes me through the backstairs of the museum to the garden. She points out the 150-year-old chestnut tree that Anne wrote about in her diary. The tree is as gnarled as anything Van Gogh painted. It is dying, propped up by steel supports. It is another fragile link to a life curtailed.

In the museum shop Anne's diary is available in umpteen languages, there are memoirs by those who knew her, there is a Hollywood film and documentary DVDs. Anne is an industry. Annelies is at the till, and I mention the house has changed. "Do you like it now?" she asks anxiously. It is a deceptively simple, tough question. Has the house lost something with its accretions, with its slick presentation? I hesitate, then, recalling the stunned reaction of the visitors, I have to say: "It is as powerful as ever." And I can barely finish because my voice cracks. Outside in the unremitting cold, the queue is still running down the street and round the corner.

On the other side of the canal I find Café Wester. It is the definition of cosy. Many of the clientele are nursing a single glass of wine, their noses buried in a book. Tea lights flicker on every table and along every shelf. Christmas decorations and fairy lights have been preserved well into January.

Outside, a grey heron struts on a houseboat. It takes off, flapping its great wings and returns to claim new territory on top of a Peugeot hot hatch, its mate circles before alighting on a more sedate Volvo estate. As it gets dark, the rain starts lashing on the double-height windows of the café. The fug that used to define Amsterdam's "brown cafes" (so named due to the smoke-stained walls) is gone – as a result of the cigarette ban. The only smoke in the café is coming from a virtual log fire, crackling in an endless video loop on a flat screen above the bar. Undemanding jazz funk and chilled house is pulsing gently in the background. All is well with the world.

But a cold damp night like this calls for more than virtual comfort. Restaurant Haesje Claes (Spuistraat 273-275) succeeds in luring me away from Prinsengracht with the promise of rich, winter warming Dutch cooking. The dark wood panelling and exposed beams of the interior look like they come with at least 300 years of certified heritage attached, but as Isabel de Haan explains, the olde worlde look is the result of the enthusiasm of her brother, Hugo, the chef-owner, for architectural salvage. Much of the first dining room's interior was rescued from skips.

The menu is unflinchingly Dutch – cheese croquets, pickled herring with potato salad, smoked eel, steaming mussels and hearty calf's liver with onions, bacon and apple. Big fat snowflakes drift down outside and settle on the cobbles – the perfect accompaniment to a supper like this.

In the morning I make my way over to the Museum and Fashion District. Opposite the Rijksmuseum, on the Museumplein, children are trying to skate on a rink under a marquee. Bright sunshine and blue skies, however, suggest the cold snap is coming to an end. The ice is no longer serviceable and the rink is halfway to becoming a paddling pool. Anxious parents are trying in vain to stop their offspring from falling over in the slush. It's good knockabout pneumonia-inducing fun.

Along the Museumplein, I approach the Van Gogh Museum, passing Japanese architect Kisho Kurokawa's Exhibition Wing, which is surprisingly jerry-built – the stone panels of the curving wall don't match up and are visibly chipped where the workmen struggled to manoeuvre them into place. The original Gerrit Rietveld-designed museum is much more successful. And the collection it houses remains jaw dropping. Here, you can chart Vincent's progress from his earliest experiments to those manic, driven, final works – his entire oeuvre spanning just 10 years.

The final wall of the permanent collection features three striking rectangular works all from 1890, the year of his suicide. Landscape at Twilight, Wheatfield With Crows and Tree Roots and Trunks – in all of them the paint seems to be liquid, dripping and almost sculptural, as if the flatness of the canvas was an unacceptable limitation. Tree Roots is the most startling – there isn't a straight line to be seen, perspective be damned. It is hurtling towards abstraction. And it is full of life.

The Real Van Gogh: the Artist and his Letters runs until 18 April 2010 at the Royal Academy (royalacademy.org.uk)

Compact Facts

How to get there

Expedia (0871 226 0808; expedia.co.uk) offers return flights with VLM Air from London City to Amsterdam, and two nights' room-only accommodation in a deluxe room at the five-star Hotel Pulitzer for £300 per person, based on two sharing.

Further information

Netherlands Board of Tourism and Conventions (holland.com).