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Regularly named one of the most expensive cities in the world, ´Üü°ù¾±³¦³ó isn’t the first place you’d think of for a bargain city break.

With its classy designer shops, once-in-a-lifetime restaurants and eye-watering entry fees, it’s easy to empty your wallet in ´Üü°ù¾±³¦³ó without much effort. Fortunately, the financial powerhouse has plenty to do for absolutely nothing as well. From stuffed sloths and succulent collections to river swimming pools and Rembrandt, here’s a guide to what to do for free in ´Üü°ù¾±³¦³ó.

1. Stroll through the tropics at the city’s Botanical Gardens

One of the best free experiences in the city is a visit to one or both of the University of ´Üü°ù¾±³¦³ó’s . The original garden, dating from 1837, sits on a hill in the city center and contains numerous exotic trees as well as a palm house and a medieval herb garden named in honor of a 16th century ´Üü°ù¾±³¦³ó doctor who knew a thing or two about medicinal plants.

Planning tip: If it looks like rain – or even if it doesn’t – head to the "new" (it was built in the 1970s) complex at Seefeld, whose domed greenhouses are the main attraction. Home to around 7000 plant species, including ferns, orchids, cacti, tulip trees and bromeliads, these steamy tropical greenhouses can belie the weather outside.

2. Time your visit right to see ´Üü°ù¾±³¦³ó’s art for free

Appreciating ´Üü°ù¾±³¦³ó’s great art for nothing is currently rather easy. The contemporary – and often controversial – Migros Museum is running an "Acts of Friendship" exhibit, which is free for all to visit until September. As for the Kunsthaus, visitors can ogle works by Rembrandt, Manet, Warhol, Van Gogh and Swiss native Giacometti for free on Wednesdays (although special exhibits still require a paid-for ticket).

Planning tip: Entry to Kunsthaus is free at all times to under 17s.

3. Explore the city by bike

´Üü°ù¾±³¦³ó is eminently walkable, but if you want to get about faster yet avoid public transportation costs, pick up a free bicycle from . You do have to pay a deposit, but it’s fully refunded when you return the bike at the end of the day. In the meantime, you have two wheels with which to explore the banks of the Limmat, the industrial maze of Züri West and – if your legs can cope – the undulating alleys of the Old Town.

4. Survey the city’s urban sprawl from the Freitag tower

For something a little less storybook, head to the industrial quarter of ´Üü°ù¾±³¦³ó West where Freitag (a homegrown brand that creates stylish bags from recycled seat belts, old tarpaulins and used bicycle inner tubes) has a flagship store made entirely of shipping containers. Its colorful tower, consisting of nine of these containers stacked one on top of another, is a modern landmark in the city and free to visit.

It’s quite a climb up the many flights of stairs to the top, and the rough, slightly rickety nature of the tower is a little unnerving, but your reward is the fascinating view – a sprawling mesh of roads, railways, warehouses and office blocks punctuated by the occasional surprise, such as the wave pool of surf center Urban Surf.

5. Take a dip in a river swimming pool

You can swim in Lake ´Üü°ù¾±³¦³ó for free, but the real action takes place in the city’s river pools. Catering to adventurous swimmers, the makes the most of a quick current, while the is a tad more relaxed with a 400m-long (1312ft) swimming canal and diving board. The historic , which opened in 1864, is on a secluded river bend but is men-only. Open to everyone is , a small island in the Limmat that is hugely popular in summer for its swimming pools, barbecue areas and grassy areas for sunbathing.

Planning tip: It's free to use the lockers, but you'll want to bring your own padlock.

6. Go birdwatching in the city center

Thanks to , ornithologists don’t have to head into the wild for some prime birdwatching; instead they can stay in the city and see a number of exotic breeds for free. Taking in injured birds since its inception in 1898, this bird sanctuary and aviary on the Mythenquai has helped rescue parakeets, toucans and everything in-between.

7. Enjoy a free drink with a knockout view at Lindenhof

The knotted narrow alleyways of ´Üü°ù¾±³¦³ó’s Old Town wend their way up to Lindenhof, an old Roman fortification with views across the Limmat River. Take a rest on a bench facing the view and quench your thirst for absolutely nada by filling up your water bottle at the pretty stone fountain – it’s just one of many across the city which provide drinking water on tap. If you’re lucky, you might even get some entertainment thrown in for nothing, too – chess and pétanque enthusiasts often come here to play.

8. Visit the University of ´Üü°ù¾±³¦³ó’s museums

Dinosaur skeletons, giant mammoths, stuffed sloths and countless insects – the hands-on is home to 1500 animals with interactive exhibits that allow visitors to listen to whales sing or get up close to insects with a magnifying glass. The university’s, (which houses fossils from the Unesco World Heritage site of Monte San Giorgio in southern Switzerland) and museum of earth sciences, , are all free too.

Planning tip: The Zoological Museum's in-house cinema shows free nature films in German twice daily.

9. Go cactus crazy at the Succulent Plant Collection

It sounds like the answer to a quiz question, but with more than 4400 species from 79 different plant families, ´Üü°ù¾±³¦³ó is home to one of the largest collections of succulents in the world. With seven greenhouses, an outdoor rockery, and cacti, agaves, aloes and pennyworts in all manner of shapes and sizes, the is free and full of surprises.

10. Visit James Joyce’s grave

The famed Irish author James Joyce wrote Ulysses in ´Üü°ù¾±³¦³ó before he died in the city in 1941. The James Joyce Foundation hosts free meetings and readings that delve into the author’s best-known works, including Finnegans Wake. Joyce is buried at the city's Kirche Fluntern graveyard, where a statue of the writer sits and thinks with a pencil in one hand and a book in the other.

11. Enter the wild in Langenberg Wildlife Park

For a break from the city, head to , west of Lake ´Üü°ù¾±³¦³ó, where the wolves, brown bears, lynxes, deer and elks roam among large forested enclosures. A 2km-long (1.2-mile-long) Forest Adventure Trail leads visitors through the forest itself via 12 interactive stations, and is accessible every day of the year, even when the visitor center is shut.

12. Climb Uetliberg, ´Üü°ù¾±³¦³ó’s mini mountain

By lofty Swiss standards, ´Üü°ù¾±³¦³ó’s local mountain Uetliberg stands nearer the shins of its contemporaries than their shoulders, but at 871m (2857ft) above sea level, the rolling, forest-roofed rumps are a pine-packed playground for hikers and bikers. It’s especially popular in autumn as its summit sits above the fog that sometimes encases the city. Climb the viewing tower for an extra special panorama.

13. Go behind the scenes at FC ´Üü°ù¾±³¦³ó

Sports fans will want to check out , which is devoted entirely to FC ´Üü°ù¾±³¦³ó. Seven themed zones trace the football club’s history since it was founded in 1896, exploring the team’s highs and lows as well as the development of football in Switzerland. It’s illustrated with photography, films, trophies and trouvailles.

Planning tip: The much bigger and flashier FIFA World Football Museum is also in ´Üü°ù¾±³¦³ó and children up to six can get in for free, however they must be accompanied by a paying adult.