The first time you go to New York, go ahead and be a sight-seer—everyone should visit the Statue of Liberty, the Met, Times Square, etc. But on a return trip, pick a neighbourhood and go deep. You’ll find hole-in-the-wall bars, great delis, quirky shops… exploring the non-touristy side of New York is an incredibly rewarding experience for a traveller.

Who cares about a little fog (okay, a lot of fog) when there’s so much to do in San Francisco? By day, explore Fisherman’s Wharf and the Aquarium of the Bay, ride a cable car, and stroll around the Presidio; by night, have a fabulous dinner (at a Michelin-starred restaurant or a tiny place in Chinatown), then hit some of the best clubs on the West Coast.

Famed for its football team and music scene, which has produced the likes of The Smiths and Oasis, this centre for sports and the arts is a down-to-earth and friendly city. The so-called Capital of the North has overcome industrial decline, bombing (in WWII and by the IRA) to become a confident and cosmopolitan city of well over two million. It is well served by a bus and light rail network. Top attractions include the Lowry art complex, arcade Affleck's Palace and Canal Street gay village.

From Shoreditch’s swaggering style to Camden’s punky vibe and chic Portobello Road, London is many worlds in one. The city’s energy means that no two days are the same. Explore royal or historic sites, tick off landmarks from your bucket list, eat and drink in exclusive Michelin-starred restaurants, enjoy a pint in a traditional pub, or get lost down winding cobbled streets and see what you stumble across – when it comes to London, the possibilities are endless.

Everyone who visits Paris for the first time probably has the same punchlist of major attractions to hit: The Louvre, Notre Dame, The Eiffel Tower, etc. Just make sure you leave some time to wander the city’s grand boulevards and eat in as many cafes, bistros and brasseries as possible. And don’t forget the shopping—whether your tastes run to Louis Vuitton or Les Puces (the flea market), you can find it here.

Amsterdam is truly a biker’s city, although pedaling along the labyrinthine streets can get a little chaotic. Stick to walking and you won’t be disappointed. The gentle canals make a perfect backdrop for exploring the Jordaan and Rembrandtplein square. Pop into the Red Light District if you must—if only so you can say you’ve been there. The Anne Frank House is one of the most moving experiences a traveller can have, and the Van Gogh Museum boasts a sensational collection of works.

Copenhagen is one of Europe’s oldest and most popular cities. It’s also one of the cleanest and most metropolitan. The dynamic Danish capital features progressive modern architecture, the must-visit Tivoli Gardens amusement park, stunning palaces, and all the activities and amenities you would expect in a world-class destination. Explore the canals and pretty narrow streets, appreciate beautiful old homes, and find great shopping and people watching on The Ströget.