Poland's capital has been voted a top 10 city to visit by Lonely Planet. Sankha Guha finds out why

Warsaw is a modern city of wide boulevards, skyscrapers, advertising hoardings, traffic jams, shopping malls and a thriving population of 1.7 million people. People live normal 21st-century lives here; they look as ordinary as the residents of Milton Keynes, and their aspirations are probably no different from MK-man.

And yet, given its recent history, the whole city is an act of will. Every day it must wake up and, against the weight of its past, Warsaw must assert its normality. And every day the nightmares are still here – under the stucco, between the cracks, in the soil. Warsaw breaks your heart. And then it breaks it again.

I am driving though a large square in the Praga district on the east side of the Wisla (aka the Vistula) with my guide Agnieszka. From my car I notice a huddle of people including a priest laying a few flowers at a small monument. "Oh we have many of these," says Agnieszka, "From the war. Where the Nazis shot maybe 50, 60 people picked up on the street as a reprisal whenever one of their soldiers was killed by the resistance." Later I learn there are more than 500 such mini-memorials in Warsaw.

The Praga district was spared the worst destruction and is one of the few places where you get a sense of what the pre-war city looked like. This is where Polanski filmed The Pianist, re-creating the Jewish ghetto, on streets such as Ulica Stalowa. It has a reputation as a dangerous area, certainly after dark. There seems little reason for tourists to venture here, but we stumble upon restaurant Pod Karpiem, at 37 Ulica Stalowa, which could serve as a perfect film-set not so much for wartime Warsaw but for the period that followed.

The untouched 1970s interior is a stylist's dream. Everything from the bare linoleum floor and plywood panelling to the lumpy carvings of jolly party folk that decorate the walls is evocative of communist-era austerity. There is little nostalgia for those times, and it's hardly surprising the local clientele stays away in droves. Proprietor Artur Wielechowski is hoping that tourists, ironically or genuinely appreciative of retro style, will book the restaurant for themed events and save his business. But I fear this address is more likely to be hosting a Starbucks in the near future.

A new bohemian set is colonising Praga and the Hoxtonisation of the area is under way. The Koneser Vodka Factory on Ulica Zabkowska still makes vodka (Zytnia, if you are interested), but it is also home to a sprawl of galleries, workshops and a theatre. The yard beyond the mock Gothic gatehouse is dotted with sculptures; most are of the rusting industrial metal variety, but among them I find Amy Winehouse. She is carved out of a single tree trunk and the somewhat literally minded sculptor Jozef Nowak has called his piece "Amy" to obviate any shred of ambiguity. Fans of Madame Tussaud will like.

A few short minutes later I am across the river in the Muranow district where the Jewish ghetto once stood. It is the scene of one of the worst crimes in history and the sheer ordinariness of the surroundings is shocking. There is nothing left. After the ghetto uprising in 1943, the Nazis did a thorough job of razing the ghetto, and then the communists, equally determined to leave no trace, went on to obliterate the site under acres of ugly tenement blocks. The ghetto occupied a third of old Warsaw; it imprisoned 400,000 Jews – and there is nothing left.

Unbelievably, there is not even a museum of the ghetto – though there is one planned (see jewishmuseum. org.pl). A few scattered monuments bear witness but they are almost by definition inadequate. A white marble memorial on Ulica Stawki marks the spot known as Umschlagplatz from where 300,000 Jews were transported to their deaths in Treblinka. The architects of the simple monument have engraved an A to Z list of first names popular among Jews at the time. There were too many; we must remember them only by their shared first names.

Somehow the Jewish cemetery on Ulica Okopowa survived the German onslaught. There are thousands of macevas (tombstones) marking graves from the past 200 years. Among them I find a wide empty circle surrounded by a series of white stones that bow inwards. The circle is concave, like a crater. This is the mass grave of some of the people who died of starvation, disease and random execution in the ghetto. As the thousands of bodies in the pit decompose, they take up less space and cause subsidence. It dawns on me that the dead don't rise from their graves to haunt us – they sink. But they still haunt us. With tears welling up, I feel numbed and curiously a part of me feels guilty – as if simply being here makes me complicit.

Later, back in Praga, I catch a jazz concert at Fabryka Trzciny. The venue is another former factory converted into an arts centre. The industrial chic of the bar recalls the complex's previous life as a marmalade and then rubber factory. Tonight, Norwegian singer Solveig Slettahjell delivers her brand of slow and deeply personal songs. But it is her unbearably poignant cover of Tom Waits's "Take It with Me" that rips the heart-strings. It is raw and beautiful and the emotion is searing. The audience melts; maybe it is my fevered imagination but they seem primed for sadness.

The Old Town is famously not old. It was rebuilt after Hitler, enraged by the Warsaw uprising in 1944 – distinct and separate from the Jewish ghetto uprising in 1943 – ordered the city's destruction with the chilling phrase "turn it into a lake". Pictures taken in 1945 show a wasteland more total than Hiroshima. This demolition, however, was meticulously planned and executed at ground level by special "Burning and Destruction" detachments of the SS. Most of the Old Town was re-created in the 10 years following the war, brick by brick, until they had a perfect full-scale working model of what used to be theirs. Standing in the rebuilt Rynek (market square), you sense the pretty "medieval" façades are built of something stronger than bricks and mortar – it is defiance.

Warsaw's resistance against overwhelming odds is celebrated in the Museum of the Uprising. It opened in 2004 on the 60th anniversary of the uprising and has rapidly established itself as the most popular museum in the city. My visit coincides with Independence Day and I jostle with parties of excited school kids who are clearly engrossed by the interactive exhibits. The subject may be grim but the atmosphere is almost party like. Despite the mind-boggling casualties – 200,000 dead – the commentary on the events of August 1944 is coolly restrained. The mask slips only once. A picture of Stalin, who ordered his army on the far side of the Wisla to do nothing while the Germans reduced the Old Town to ashes, carries the caption, "Joseph Stalin, the embodiment of evil". It is a rare glimpse of Warsaw's rage.

The national holiday also brings out the crowds to the city's biggest green space, Lazienki Park. Sometimes derided as grey and dull, Warsaw is, in fact, blessed with a generous quota of parks. Parents are enjoying a lazy stroll while their children stalk the free-range peacocks to get a snapshot on their mobile phones. Dogs are walked and lovers are embraced.

The Museum for Contemporary Art is housed in Zamek Ujazdowski, a castle that overlooks the park. It is closed today but some of the conceptual art is outside. I find a series of marble benches engraved with wannabe aphorisms. An example: "Silly holes in people are for breeding or are from shooting." Most have the taint of smart-arseness about them. But the last line on one bench catches my attention: "It is in your self interest to find a way to be very tender." Elsewhere, such ham-fisted irony might seem glib. In Warsaw it is the lesson of history.

Compact facts

How to get there

Cox & Kings (020-7873 5000; coxandkings.co.uk ) offers a three-night break at Le Regina Hotel in Warsaw from £485 per person, based on two sharing, including return flights with British Airways, private transfers and B&B.