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.

Modern myth has it that these days everyone in Los Angeles has written a screenplay, is writing a screenplay or is just visiting. For those in the latter category we offer a road map of ideas to help make a trip to this ultra-hip, ultra-happening haven easy, fun and exciting. While LA will always be associated with movies and movie stars, it is also a culturally vibrant city that boasts a range of interesting attractions from prestigious art museums and galleries to fabulous theatre, both well-known productions and smaller fringe shows. Art enthusiasts will be stunned by the extensive collections at the J. Paul Getty Center and the Los Angeles County Museum of Art. Visit the La Brea Tar Pits on Museum Row, then investigate the trendy shops on Melrose Avenue. Families will not want to miss the zoo or the action at Universal Studios Hollywood. Of course, no trip to LA would be complete without a stop at the Venice Beach Boardwalk or a visit to Mann's Chinese Theater and the Walk of Fame.

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.

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.

Many people travel through Frankfurt for business, as it's a major transportation hub and an industrial and financial metropolis. Of course we know that business travellers hate to have any fun on the road (wink), but it's worth lingering in Frankfurt if you can. The 2,000-year-old city has much to offer: skyscrapers, the Main River, a famous opera house, thriving theatre district, zoo, pedestrian shopping street, parks, scores of bars and dance clubs, and more than 50 museums.

Lucerne is an ancient town with strikingly modern sensibilities. One of Europe’s oldest covered bridges serves as its centrepiece, and fresco-adorned historic houses line the streets, but it’s also home to the cutting-edge KKL, a concert hall and art gallery. Take the cableways up the Pilatus, Stanserhorn or Rigi mountains for breathtaking views, or see Lake Lucerne on a steamship cruise.

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.

The largest city in Switzerland is a major contemporary art and shopping destination. Important artworks are displayed in the Kunsthaus and the Rietberg Museum. Those who consider shopping an art can hone their skills along Bahnhofstrasse and Niederdorf. Chagall's stained-glass windows in the Fraumünster amaze. Zurich's 500 clubs and bars, including several in swimming pools, pulse with life till the early hours. This city on Lake Zurich has excellent public transport and a free bike-hire system.

Munich was almost completely destroyed in two world wars, yet it's managed to recreate much of its folkloric, Bavarian past. Oktoberfest is legendary, but you can visit the Hofbrauhaus any time of year for an immense beer. Olympiapark, the site of the 1972 games, is not to be missed (you can skate on the Olympic ice rink and swim in the pool). On a somber note, take time to visit the concentration camp at Dachau—it's an intense, yet unforgettable, glimpse into the not-too-distant horrors of the Holocaust.