If your mental image of the German capital derives from war films or spy stories, prepare to be pleasantly surprised by one of the greenest cities in Europe. And if you’re looking to release the inner hedonist, you’ll find nightlife that carries on through until morning and a gay scene that’s unusually shameless. While the city has always been a bolthole for the unconventional, today it’s also a major cultural centre, combining top-flight museums, galleries and concert halls with thriving alternative arts and music scenes.

Most unmissable sights are in and around central Mitte. The east-west axis of Unter den Linden is a good place to start. Frequent buses run the length of the tree-flanked boulevard, linking it with Bahnhof Zoo in the west. The western end is marked by the iconic Brandenburg Gate, once closed off between East and West Berlin, which leads on to the huge Tiergarten park. North- west of the Gate is the government quarter and the revamped Reichstag, crowned by Norman Foster’s magnificent glass cupola (Platz der Republik, 2273 2152, www.bundestag.de). Trips to the top are free, and the view is magnificent, but expect to queue. To the south side of the Brandenburg Gate is the recently completed Memorial to the Murdered Jews of Europe (Cora-Berliner-Strasse 1, 2639 4336, www.holocaust-denkmal.de). The controversial design by Peter Eisenmann has 2,700 columns of varying heights in an undulating space the size of a city block.

South of Unter den Linden is Gendarmenmarkt. Topped and tailed by the German Cathedral (Deutscher Dom, 2273 0431, closed Mon) and the French Cathedral (Französischer Dom, 229 1760, closed Mon), it is one of Berlin’s most beautiful squares. At the eastern end of Unter den Linden is Museum Island (Museumsinsel), a UNESCO World Heritage Site whose clutch of superb collections includes the Pergamonmuseum (Am Kupfergraben, 2090 5577, www.smb.spk-berlin.de, closed Mon), incorporating the Babylonian Gate of Ishtar. The majestically porticoed Altes Museum (Lustgarten, 2090 5577, www.museen-berlin.de) and the 19th-century art at the Alte Nationalgalerie (Bodestrasse 1-3, 2090 5801, www.museen-berlin.de, closed Mon) are also worthwhile. Other attractions are the Berliner Dom (Am Luftgarten, 2026 9128, www.berliner-dom.de) and Deutsches Historisches Museum (Zeughaus, Unter den Linden 2, 203 040, www.dhm.de), which has a swanky new wing by IM Pei.

Eastwards is the communist-era concrete expanse of Alexanderplatz, and the landmark ball-and-spike TV Tower (Fernsehturm, 242 3333, www.berlinerfernsehturm.de), with a revolving observation deck; south are the reconstructed medieval Nikolaiviertel and remnants of the original medieval wall.

North of Alexanderplatz, the renovated Scheunenviertel (‘Barn Quarter’) is packed with galleries, bars and shops. Its focal point is the Hackesche Höfe, a warren of jugendstil (art nouveau) courtyards full of boutiques and cafés. Nearby Auguststrasse is the art scene’s main drag, while the revived Jewish Quarter centres on the Neue Synagoge (Oranienburger Strasse 28-30, 8802 8451, www.cjudaicum.de, closed Sat).

Prenzlauer Berg has gentrified rapidly and, though containing few specific sights, is a relaxed area for a meal or a drink. Friedrichshain has a more communist and post-industrial feel. The lively, youthful nightlife around Muhlenstrasse and Simon-Dach-Strasse contrasts with the eerily wide main drag, Karl-Mar x-Allee, which is a treat for fans of Stalinist architecture.

Once Berlin’s nonconformist heart, Kreuzberg remains fascinatingly diverse. Its museums include the exhibit about the Berlin Wall at the Haus am Checkpoint Charlie (Friedrichstrasse 43-45, 2537 250, www.mauer-museum.com), and the Daniel Libeskind-designed Jewish Museum (Lindenstrasse 9-14, 2599 3300, www.jmberlin.de), where the remarkable deconstructivist building almost upstages the already quite memorable exhibition within.

Neighbouring Schöneberg offers some great bars in its northern reaches, and is the hub of Berlin’s thriving gay district.

Tiergarten is dominated by the park of the same name. At its south-east corner is a clutch of museums, including the Mies Van der Rohe-designed Neue Nationalgalerie (Potsdamer Strasse 50, 266 2651, www.museen-berlin.de, closed Mon) and the Filmmuseum Berlin (Potsdamer Strasse 2, 300 9030, www.filmmuseum-berlin.de, closed Mon). The latter is in the new complex at Potsdamer Platz, among buildings from famous architects such as Richard Rogers and Renzo Piano. At the south-west corner of Tiergarten is the beautifully landscaped Zoo and Aquarium (Hardenbergplatz 8, 254 010, www.zoo-berlin.de).

To the south-west lie the vast Grunewald woods, the watery pleasures of the Wannsee and assorted smaller lakes – Strandbad Wannsee is Europe’s largest inland beach – and the Dahlem museum complex. The extensive and authoritative Ethnologisches Museum (Lansstrasse 8, 830 1438, www.smb.spk-berlin.de, closed Mon) is remarkable in itself, but the same building also houses terrific museums of Indian Art, East Asian Art and European Culture. Heading south-east, you can drink in the villagey charms of Köpenick, or sample at your leisure the products of the Berliner Burgerbräu brewery at Friedrichshagen, which throws open its gates for an annual summer beer festival. Boat trips can be taken on the nearby Muggelsee.

• Tourist information: Europa-Center, Budapester Strasse, Charlottenburg (250 025, from outside Germany 01805 754 040, www.btm.de).