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.

Central Dalmatia is the most action-packed and diverse part of Croatia, with pretty islands, quiet ports, rugged mountains, numerous castles and an emerging culinary scene, as well as three Unesco World Heritage sites: Diocletian’s Palace in Split, the medieval walled town of Trogir and the ancient strip fields of the Stari Grad plain on the island of Hvar. Throughout it all, the rugged 1500m-high Dinaric Range provides a dramatic background.

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.

While it might lack the world-class cultural institutions of Berlin, Belgrade, at the confluence of the Sava and Danube rivers, offers its own distinctive appeal, with storybook historical districts and venerable fortresses and parks. Better still, this center of Slavic cool just got much easier to reach: Direct flights from North America, via New York City, started in June on Air Serbia. Throw in Belgrade’s cafe scene, low prices, talented young designers, emerging former industrial districts, sausage-filled cuisine and unbridled night life — from D.J. bars to party boats to all-hours nightclubs — and the comparison seems even more compelling.

The earliest structures in the colony were built to the bare minimum of standards. Upon his appointment, Governor Lachlan Macquarie set ambitious targets for the architectural design of new construction projects. The city now has a world heritage listed building, several national heritage listed buildings, and dozens of Commonwealth heritage listed buildings as evidence of the survival of Macquarie's ideals.

A trip to Rome is as much about lapping up the dolce vita lifestyle as gorging on art and culture. Idling around picturesque streets, whiling away hours at streetside cafes, people-watching on pretty piazzas – these are all an integral part of the Roman experience. The tempo rises as the heat of the day gives way to the evening cool and the fashionably dressed aperitivo (pre-dinner drinks) crowd descends on the city's bars and cafes.

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.

Sci-fi Cityscapes

Tokyo’s neon-lit streetscapes still look like a sci-fi film set – and that’s a vision of the city from the 1980s. Tokyo has been building ever since, pushing the boundaries of what’s possible on densely populated, earthquake-prone land, adding ever taller, sleeker structures. Come see the utopian mega-malls, the edgy designer boutiques from Japan’s award-winning architects, and the world’s tallest tower – Tokyo Sky Tree – a twisting spire that draws on ancient building techniques. Stand atop one of Tokyo’s skyscrapers and look out over the city at night to see it blinking like the control panel of a starship, stretching all the way to the horizon.

The Shogun’s City

Tokyo may be forever reaching into the future but you can still see traces of the shogun’s capital on the kabuki stage, at a sumo tournament or under the cherry blossoms. It’s a modern city built on old patterns, and in the shadows of skyscrapers you can find anachronistic wooden shanty bars and quiet alleys, raucous traditional festivals and lantern-lit yakitori (grilled chicken) stands. In older neighbourhoods you can shop for handicrafts made just as they have been for centuries, or wander down cobblestone lanes where geisha once trod.

Eat Your Heart Out

Yes, Tokyo has more Michelin stars than any other city. Yes, Japanese cuisine has been added to the Unesco Intangible Cultural Heritage list. But that’s not what makes dining in Tokyo such an amazing experience. What really counts is the city’s long-standing artisan culture. You can splash out on the best sushi of your life, made by one of the city’s legendary chefs using the freshest, seasonal market ingredients. You can also spend ¥800 on a bowl of noodles made with the same care and exacting attention to detail, from a recipe honed through decades of experience.

Fashion & Pop Culture

From giant robots to saucer-eyed schoolgirls to a certain, ubiquitous kitty, Japanese pop culture is a phenomenon that has reached far around the world. Tokyo is the country’s pop-culture laboratory, where new trends grow legs. Come see the latest looks bubbling out of the backstreets of Harajuku, the hottest pop stars projected on the giant video screens in Shibuya, or the newest anime and manga flying off the shelves in Akihabara. Gawk at the giant statues of Godzilla; shop for your favourite character goods; or pick up some style inspiration just walking down the street.