Think you’re done sightseeing? Think again. Europe’s most popular cities have all sorts of weird and wonderful delights in addition to the big-name attractions. Find time to seek out these oddities and you’re bound to feel better acquainted with the place – albeit a little bewildered. 

Click through the gallery to discover 30 of our favourite strange sights in Europe's urban hubs...

An extraordinary example of high-rise, interactive art, Colour by Numbers is a light installation in Stockholm’s Telefonplan tower. Passers-by can operate the lights illuminating different floors using their smartphones, via a call or with an app. Red, green and blue can be mixed to create a customised colour and your very own temporary light show.

Within the lavish Palazzo dell’Archiginnasio, part of the world’s oldest university, you’ll find a splendid, 17th-century cedar-wood lecture theatre. The room’s decorations, including anatomical models and statues of notable physicians, hint at its purpose: students gathered here to watch human and animal dissections. The tiered seating and compact size ensured everyone had a good view – including the unfortunate corpse, which would have been laid flat on the central marble table.

Locks of hair, Valentine’s Day cards, a prosthetic leg…The Museum of Broken Relationships provides a home for the detritus – some surprising, some tear-jerking, some downright bizarre – of past relationships. Conceived by former couple Olinka Vištica and Dražen Grubišić in 2006, the collection has resonated with the lovelorn worldwide. The museum has toured internationally, from Melbourne to Mexico City, with its collection growing all the time.

Le Marais in Paris is prime flâneur (loafer) territory, with its pretty cobbled streets, buzzing bars and boutiques full of oh-so-desirable objects. As you potter in the northwestern reaches of the quartier, keep your eyes peeled for a head-scratching work of street art. At 1bis rue Chapon, a nondescript, often graffiti-clad, dark-green door is accompanied by an intriguing sign reading ‘J.B. & S.B. Specialistes’. Specialists in what? Micro-office working? Swinging cats? In fact, the whole facade is a trompe l’oeil, the work of artist Julien Berthier. 

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Manneken Pis – that little lad caught short, cast in bronze – is Brussels’ mascot and a must-see for most tourists. Perhaps it’s not surprising then, in a nation famed for its comics, that the wee fellow has spawned various counterparts across town. There’s the female equivalent, Jeanneke Pis, and a less well-known canine addition. The cock-legged Het Zinneke (Zinneke literally means ‘mongrel’, but is also used to describe a person from Brussels) can be spotted on rue des Chartreux.

Acclaimed Danish artist Olafur Elliason is behind this spiral-staircase sculpture in the entrance of the KPMG building in Munich. The stairs wind up and round in a double-helix shape, ultimately leading nowhere – could this be a comment on the accountancy work going on in the surrounding offices? Or about life itself? It's an enigma to discuss over a Weissbier or two.

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Suffering gallery fatigue after visiting the Museo Guggenheim? Wander the atmospheric streets of Bilbao and stop for refreshment at this water fountain. ‘La Fuente del Perro’ ('perro' means 'dog' in Spanish) is in fact a misnomer. The 19th-century fountain was designed with ancient Egypt in mind, and those little pups were meant to be lions. Either way, the fresh water that gushes from their mouths is welcome and the much-loved fountain has given the street its name.

Stifle your giggles. Iceland is presented in all its glory at this museum in Reykjavík, with more than 215 penises and penile parts from almost all of the country’s land and sea mammals. From whales to reindeer, polar bears to mice, that’s quite a collection. Homo sapiens are represented, too, and a handful of keen chaps have pledged to bequeath their own bits when the time comes. Signed certificates are on display, so there’s no going back now.

This charming park lets you sightsee across Portugal, and beyond to other Portuguese-speaking nations, all in a single visit. Carefully crafted miniature versions of landmarks, monuments and models of regional houses can be peered into and clambered over to your heart’s content. Once the Gulliver fantasy starts to wear off, head back into central Coimbra to admire some of the real things. 

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Hard to miss on the busy Promenade des Arts, the huge, square-headed La Tête Carrée houses three floors lined with books, as part of Nice’s central municipal library. The sculpture’s inherent message is also striking: it’s subtitled ‘Thinking inside the box’. The structure is unusual not just for its immense size – 98 feet (30m) high and 45 feet (14m) wide – but also because it's an occupied public sculpture. Come nightfall, you can make out the illuminated interior.

Superb skiing, placid lakes and fondue are usually top of the agenda in Switzerland. Succulents and cacti maybe less so. Who would have thought these arid-loving specimens would find a home here? In fact, the Succulent Plant Collection is one of the largest in the world and attracts botanists and collectors from far and wide. Join them for some free, unparalleled house-plant inspiration and, if you time it right, for a glimpse of the nocturnal-flowering Queen of the Night cactus.

Horses are common, yes, but it’s not often you see bears commemorated in military statues. There’s quite a story behind this bronze in Princes Street Gardens in central Edinburgh. Adopted as a cub by Polish soldiers, Wojtek the bear went on to serve in the Second World War as part of the 22nd Artillery Transport Company of the II Corps. He lived out the rest of his days in Edinburgh Zoo.

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Sniff out this eccentric sight within the leafy, medieval surrounds of Lund University. The Nose Academy forms part of the Museum of Student Life – noses, like strong livers, are apparently deemed essential parts of Swedish studentdom. Here you can see more than 100 plaster casts of the noses of eminent Scandinavians. Displays include that of Sweden’s first astronaut, Christer Fuglesang, and the silver prosthetic nose of 17th-century astronomer Tycho Brahe, who lost the bridge of his conk in a duel.

Largely hidden from view, behind the park gatekeeper’s cottage on Bayswater Road in London, there lies a touching resting place for hundreds of beloved Victorian-era pets. Just possible to make out through the railings – or close up on one of the occasional organised tours – are heartfelt tributes to local residents’ mostly canine companions. There is also a long-gone cat, several birds and even a monkey. 

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Holding one of the largest collections of neon signs in Europe, the Neon Museum is located in Warsaw's hip Soho Factory, a creative space carved out of an industrial district. It commemorates the neon signs of communist times, many of which are somewhat prosaic, announcing such things as 'dancing' or 'sewing machines'. Of course, private businesses were non-existent in the post-Stalin era, so there were no big brand names to light up the streets.

Prepare to confront your own mortality, again and again and again, at the crypts beneath Rome's Santa Maria della Concezione. In the mid-18th century, the resident Capuchin monks embarked on the macabre task of decorating the six crypts with the bones of their departed brethren. It took them almost 50 years and the result was intended to be a meditation on the transience of life. Some might find the experience more chilling than contemplative. 

Everyone associates Amsterdam with its canals, but you don’t expect to find a watery wonderland indoors. The arched Beurspassage, which runs between Nieuwendijk and Damrak, has been flamboyantly transformed into a living work of art known as Oersoep. It's by a trio of artists – Arno Coenen, Iris Roskam and Hans van Bentem – and it celebrates the water that flows through Amsterdam, and its role in the city’s history. Expect a rich confection of mosaics, paintings, mirrors and upcycled chandeliers.

If you want to escape Kraków’s Old Town crowds – and you’re up for a challenge – add this kitsch Elvis Presley monument to your itinerary. Beside a footpath (Aleja Elvisa Presleya, or Elvis Presley Avenue), on the edge of the Zakrzówek woods, an arresting portrait of The King awaits. Set in silicone and placed in the hollow of a gnarly standing stone, this is the work of the city’s Elvis fan club.

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Bringing to mind a fairy tale or the tree creatures in The Lord of the Rings, this ravenous plane tree in the grounds of Dublin’s King’s Inns law school is gradually gobbling up a nearby bench. City councillors have called for the 80-year-old tree to be protected but, given its location in Ireland’s oldest law school and its monstrous appetite, it can probably look after itself.

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Put down your smartphone and hark back to 1900, when a shipwreck off the Greek island of Antikythera was first discovered. Now, zoom back another 2,000 years and consider the ancient Greek expertise that created the ‘analogue computer’ that divers salvaged. Fragments of the Antikythera Mechanism are held in the Bronze Collection of the National Archaeological Museum of Athens, along with artistic reconstructions of how this complex device for predicting astronomical positions and eclipses might have looked and worked.

Copenhagen isn’t short of architectural marvels, but head away from the busy city centre to be confronted with this unexpected public park. In the multicultural Norrebro district, a half-mile stretch has been jointly designed by artists and landscape architects with the aim of celebrating the neighbourhood's diversity. The shocking pink, red and orange of the Red Square can’t fail to get tongues wagging, and objects here have been sourced from across the globe. You'll find litter bins from the UK, a fountain from Morocco, manhole covers from Zanzibar and these swing seats from Baghdad.

The imposing Pile Gate, dating from 1537, is the starting point for most Dubrovnik strolls. As you pass through and head along the pedestrian promenade of Stradun, keep an eye out for a cheeky-looking gargoyle. He protrudes on the left at approximately ankle level, near the steps leading up to the city walls. It’s by no means easy, but if you can perch on his well-worn head and take off your shirt – keeping your balance all the while – it’s said you will be lucky in love.

When you’ve taken in the splendid views from the dome of the Basilica of St Stephen, head to the second floor’s treasury of ecclesiastical objects. Here you’ll find the chapel of the Holy Right, the basilica’s big draw. Inside is the mummified right hand of St Stephen, founder of Hungary, held in a wizened, tight fist. The relic is paraded each August on St Stephen’s Day. Spare a 200Ft coin and the ornate reliquary will be momentarily illuminated.

Utterly transfixing, yet deadly poisonous, Alexander Calder’s Mercury Fountain was commissioned by the Spanish Republican government for display at the 1937 World Exhibition. As with Picasso’s renowned Guernica, the artwork represented a protest against Franco’s regime. Troops had attacked the major mercury mine in Almadén. At this time, the lethal properties of mercury were not fully understood. Today, the fountain is displayed behind safety glass at the Fundacio Joan Miró in Barcelona.

Chic residents, tempting markets and a beguiling medieval old town draw the hordes to Aix-en-Provence. Before the city was home to Paul Cézanne and Émile Zola, a certain Monsieur d’Albertas unwittingly bought himself a grand house in a street with an insalubrious history. If he’d inspected the wrought-iron balconies more closely, perhaps he might have twigged – the phallic designs were a discreet(ish) indication of the business going on inside.

This is not just a David Hasselhoff Museum, it's a hidden David Hasselhoff Museum. Little documented, born of a tongue-in-cheek shrine and secreted in the basement of Circus Hostel, it’s the stuff of urban legend, as perhaps befits the Baywatch and Knight Rider star. The Hoff’s strong connection with the German capital was bolstered with his rendition of ‘Looking for Freedom’ at the New Year’s Eve concert held at the Berlin Wall in 1989, weeks after its fall.

A heartwarming antidote to disposable consumer culture, Lisbon’s doll hospital has been mending (or curing) its toy patients for almost 200 years. It’s a family-run labour of love, with each case given due consideration and deemed as unique as the doll, or its owner. Admittedly, the business now extends to repairs of Barbies as well as antique porcelain dolls. Unclaimed patients and various parts – lost limbs, glassy eyeballs, plump-cheeked heads – form an unlikely, wistful museum collection. 

You might walk right past the Kamppi Chapel, a wooden, wax-treated, cocoon-like structure. It has the air of a fancy office building, or a bewildering piece of public art, perhaps. In fact, the curvilinear masterpiece is a Lutheran chapel, open to all faiths and offering a welcome respite from the determined shoppers and busy daytime activity outside. Weird-looking? Yes. Wonderful? Definitely.

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Prague’s Dancing House is a striking partner to the neighbouring 18th- and 19th-century buildings. Arising from post-Second World War rubble, it took a long time to take shape under the direction of Vlado Milunić and Frank Gehry, finally being completed in 1996. The two clinching columns were initially known as Fred and Ginger. While its original destiny as a cultural centre never materialised, it does now house an art gallery, rooftop restaurant and a high-end hotel.

An art installation with a scientific bent, the Cyanometer by Martin Bricelj Baraga is a glinting, glass and stainless-steel monolith standing in central Ljubljana. Inspired by Horace-Bénédict de Saussure’s original 1789 cyanometer – a device used to measure the blueness of the sky and thus predict the weather – Baraga’s modern, solar-powered version uses the same criteria to measure air quality. 

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