Along the Atlantic, the Beira Litoral lures surfers and sunseekers with scores of sandy beaches. Here, the sophisticated university city of Coimbra and the brash casino-party town of Figueira da Foz arm-wrestle for visitors’ attention. Move inland to the Beira Alta highlands and the mood shifts entirely. Stoic stone villages cling to the slopes of Portugal’s highest mountains – the Serra da Estrela – and cast their gaze down at the fertile wine country of the Dão valley.

Oslo is blessed with some incredibly beautiful parks which manage, in typical Norwegian style, to straddle the line between a bucolic naturalness and well-kept grace. As soon as the sun is out this is where you'll find locals lolling, picnicking and often getting their gear off and catching some rays.

This is a city that staged a revolution, was headquartered by Nazis, bombed to bits, divided in two and finally reunited – and that was just in the 20th century! Walk along remnants of the Berlin Wall, marvel at the splendour of a Prussian palace, visit Checkpoint Charlie or stand in the very room where the Holocaust was planned. Berlin is like an endlessly fascinating 3D textbook where the past is very much present wherever you go.

Tokyo feels limitless in size and scope and often seems more like a collection of cities than one cohesive whole. At the centre is the Imperial Palace. To the east of the palace is the old city, the historic downtown that came to life during the feudal era (when a castle stood where the palace is today). Here, in neighbourhoods like Ueno and Asakusa, the attractions have a more traditional slant: there are museums, shrines and temples, historic restaurants and artisan workshops.

Immersed in history, London's rich seams of eye-opening antiquity are everywhere. The city's buildings are striking milestones in a unique and beguiling biography, and a great many of them – the Tower of London, Westminster Abbey, Big Ben – are instantly recognisable landmarks. There’s more than enough innovation (the Shard, the Tate Modern extension, the planned Garden Bridge) to put a crackle in the air, but it never drowns out London’s seasoned, centuries-old narrative.

The Castle District encompasses Castle Hill (Várhegy) – nerve centre of Budapest’s history and packed with many of the capital’s most important museums and other attractions – as well as ground-level Víziváros (Watertown). What the latter lacks in sights it makes up for in excellent restaurants, many of them around Széll Kálmán tér, a major transport hub and the centre of urban Buda.