"Ich bin ein Berliner" President JF Kennedy declared during his 1963 visit to the then divided city of Berlin.

After spending a long weekend in the German capital I can echo his sentiment – few places get under the skin quite like this sprawling, cosmopolitan, beautifully ugly metropolis that was the tumultuous epicentre of some of 20th century Europe's most historic and horrific events.

Befitting a place that is split by a river and spent three decades divided by a wall and ideologies, Berlin is a city of contrasts. Stunningly restored baroque architecture vies for the attention with graffiti-clad tenements; pristinely clean thoroughfares are fringed by crumbling squats which are home to the city's infamous impromptu club scene; lush green parks, lakes, rivers and opulent imperial palaces are juxtaposed with utilitarian concrete carbuncles from the communist era.

Nearly two decades after the wall finally came crashing down, differences between the former east and west sides of the city can still be felt.

We stayed at the Circus Hostel – a funky mecca for backpackers – in Rosenthaler Platz in Mitte, the central district, an area once east of the wall. While The Circus has become something of an institution for the hordes of young travellers who flock to Berlin for its combination of cutting-edge nightlife, history and culture, its stylish penthouse apartment – with stunning views across the roofscape – made an ideal base from which to explore the city.

During the communist era this area was once a hotchpotch of squats and near-derelict buildings. Today it is a thriving, rejuvenated, city neighbourhood, home to independent designer stores in the Hackescher Markt area and a glut of bars, clubs restaurants – but it still possesses a healthy dash of the almost-designer urban decay that helps give Berlin its reputation as an uber-cool capital of shabby chic.

While Berlin is huge, navigating your way around the city centre on foot is relatively easy, with the huge TV Tower at Alexanderplatz – the centre of the former East of the city – providing a handy beacon for orientating oneself. This space-age spire, built by the communists largely as a single-digit "salute" to those on the Western side of the wall, can been seen from virtually all over the central part of the city.

However utilising public transport is a must if you are to make the most of your visit. A Berlin Welcome Card, gives you unlimited use of the transport network and discount vouchers and, if upgraded, free entry to many of the city's 170 museums and galleries.

Even if you don't have the time or the inclination to visit Berlin's world-renowned collection of museums on an island in the River Spree, the Museuminsel should be visited just to take in the fantastic neo-renaissance architecture of the museums and the grandiose Baroque beauty of the Berliner Dom, Berlin's biggest cathedral.

Largely destroyed by RAF and then the Russian land army during the Battle of Berlin, most buildings on the Museuminsel have, since the wall came down, been restored to their former glory – but the Neues Museum, under the guidance of English architect David Chipperfield, has had parts of it left in a war-torn state so that the museum itself becomes part of the history on display.

A short stroll from the Museuminsel, past former imperial palaces and the site of Hitler's book bonfire, is the famous Brandenburg Gate and the neighbouring Bundestag, the home of the German parliament, which now convenes under a stunning glass dome designed by architect Norman Foster. Formerly known as the Reichstag, the building was in ruins before the Second World War after a fire that the Nazis blamed on communist terrorists and used as justification for the suspension of civil liberties and the creation of a one-party Nazi State.

The horrors that followed would leave an entire continent in ruins, millions dead and result in the city of Berlin being carved up between the East and the West and eventually divided by the Communist wall – the physical embodiment of the Cold War's Iron Curtain. A one kilometre section of the wall, now painted in dozens of murals espousing freedom and tolerance, forms the East Side Gallery between the stunning Oberbaumbrücke (Oberbaum Bridge) and the Ostbahnhof railway station.

Berlin today appears to be a city determined to ensure the past isn't repeated. It is rich in symbolism like the aforementioned Bundestag's glass dome, which is designed to give the parliamentary proceedings inside at least an air of transparency.

The city puts it scars on display and is unflinching in its portrayal of a history that shamed a nation, as exemplified by the Holocaust Memorial – another must-see landmark. The memorial, situated next to the site of Hitler's command bunker, covers an entire city block in an undulating grid of coffin-sized concrete blocks of differing heights that really do produce an eerie feeling of foreboding, helplessness and confusion as one wanders among them.

Adjacent to this is the new Berlin – Potsdamer Platz – a sleek selection of glass and brick skyscrapers built upon what was once the centre of Berlin's pre-war high society decadence, but became a bombed-out and bulldozed no-man's land after the erection of the wall.

History buffs will revel in a city that has shaped the modern political landscape of an entire continent, but culture vultures of all varieties will also find Berlin has much to offer. The city has been the muse of the likes of U2 (a name they share with/stole from one of Berlin's U-Bahn lines), David Bowie and Lou Reed – and is now the spiritual home to the techno dance scene as well as one of world's most acclaimed philharmonic orchestras.

And while gastronauts will find their appetites satiated in top class restaurants of every hue, lovers of fast food will be in their element as this is a city stuffed full of street food. Berlin lays claim to being the inventor of the doner kebab and hawkers carrying portable barbecues sell sizzling-hot sausages in most public squares. However, it is currywurst – a gut-rotting concoction consisting of sliced bratwurst swimming in ketchup and smothered in curry powder and paprika – that is the city's real signature dish; to the extent that it even has a museum in its honour.

This eclectic culinary creation can, perhaps, be used as a metaphor for the city itself. While it may look and sound unappetising (and, to be fair, parts will probably leave a bad taste in your mouth) beneath the surface it is succulent, satisfying and full of flavour. It is industrial and robust, yet also exotic and cathartic – and it is certainly not easily forgotten. And it truly does, as a band named Berlin sang on the Top Gun soundtrack, take your breath away.