This grand cathedral is the most striking feature of the Florence skyline and given work on the structure spanned two centuries thanks to the late addition of the egg-shaped dome, so it should be. Though tickets are required to explore some parts of the Renaissance church, including the octagonal dome, it’s free to enter the dimly lit interiors and crane your neck at the frescos that adorn the ceiling.

Strap on some comfortable shoes; Budapest is a city made for power walking. There are eight key bridges that cross the Danube. Each provides a different view of the opposing physical sides of the city and reveals a snippet of its history. While it’s a solid trek to tick off all eight in one day, you can hit half in around an hour if you start at the Szencheny Chain Bridge and walk towards the Petofi Bridge.

Fairytales have come to life on the outskirts of the Danish capital in the form of six enormous giants constructed out of recycled wood. Some are hiding in the forest, others are tucked beneath a bridge – make a day of seeking them out with your kids.

Visit at low tide and this oceanic instrument looks like a set of stairs trailing into the sea but as the water rises and waves lap at each step, it transforms into something else entirely. Within the stairs, designed by architect Nikola Bašić, are pipes that produce seven different chords as the sea pushes air and water inside the cavities, creating a mournful lament, reminiscent of a whale call echoing around the seafront.

This centuries-old affair is one of the most recognisable traditions linked to the royal family. A 45-minute display of pomp that begins at Buckingham Palace at 11am on Mondays, Wednesdays, Friday and Sundays, you’ll witness one group of The Queens Guard, adorned with their tall bearskin hats, officially hand over their protection duties to the next.

The country’s most beloved 2D characters have been permanently painted on the sides of shopfronts, the walls of homes and, really, any available flat surface available in homage to the comic-strip art form. You can find one of the most famous Belgian characters, Tintin, on a wall on Rue de l’Etuve. 

If you want to peek at the Mona Lisa without handing over the usual 22€ (AU$36) admission fee then a little planning is required. It’s free to meander through the hallowed halls that house some of the world’s most iconic artworks on the first Friday of the month after 6pm (except in July and August). Entry is also free on 14 July, Bastille Day. 

What’s lunch without a side of classical music? There’s a free concert at the Concertgebouw, an exquisite concert hall bordering the Museumplein Park, every Wednesday (excluding July and August) at lunchtime that runs for around 30 minutes. The program changes every week and covers off a varied line-up of classical artists, chamber music and young performers. Seats are limited so you will need to nab an admission ticket prior to the performance.

It’s been nearly 30 years since this former symbol of oppression was transformed into one of the most celebrated stretches of art in the world thanks to 118 politically charged artists from 21 different countries who were determined to turn the Berlin Wall into a thing of beauty.

You’ll have to allocate a few koruna to walk through the great green doors of St Vitus Cathedral and the associated Prague Castle but it’s free to traipse around the central square and admire the exterior architecture of the UNESCO World Heritage site, which is more than 1000 years old in some well-maintained sections.

The final resting place of revered figures, including Jim Morrison, Oscar Wilde, Edith Piaf and Marcel Proust, this gigantic cemetery is worth an afternoon wander to marvel at the ways we remember those we have loved. Eerily peaceful, with more than 70,000 burial plots across the 44 hectares, all it will cost is the metro fare to the station of the same name.

There are thousands of tonnes of glass in the orb adorning Germany’s key parliamentary building and, from your vantage point on the building’s roof, you peer down through it into the lower assembly hall. It will take around 20 minutes for you to ascend and circle the roof, all the while listening to an audio guide that points out key sights you can see from your position. Admission to the roof is free but advance registration is required via the building’s website.

This windswept town and the surrounding capes on the south-western tip of Portugal’s Algarve region were once thought to be the place where the world ended and if you stand – safely – on the edge of one of the vertiginous cliffs and stare out at the seemingly endless ocean, you can understand why ancient navigators considered it so.

Yes, you have to pay for your ticket onto the subway but the incredible underground art exhibition (that can, at times, feel like a technicolour cocoon) is totally free of charge. Ninety per cent of the city’s stations feature an artwork – whether that be a painting, engraving or installation. Visit Stockholm has a guide to some of the best.

Consider this quaint puppet show a crash course in German folklore. Each day at 11am and midday, the 32 rotating figures come to life for 15 minutes and re-enact the Middle Ages wedding ceremony of Duke Wilhelm V to Renata of Lorraine, as well as a jousting tournament and a well-known German jig. Attached to the side of the town hall in central Marienplatz, it’s a sweet addition to your itinerary before fronting up to a beer hall.

The rocky shores of this summer playground are a perfect place to enjoy the sun but if you tire of tanning, head east to Parc du Mont Boron, an elevated public park with sweeping views of the ragged coastline. There are 11 kilometres of footpaths throughout the 57-hectare park fringed by olive trees and Alesso pines, as well as a 16th century castle.

To wander around the Royal Tombs, Shrine and Poet’s Corner within the grand Westminster Abbey does require payment but to sit in quiet contemplation during a service is, of course, free. Attend the daily 5pm evening service held in the Quire – you’ll recognise the checked marble floor – and it will truly feel like stepping back in time thanks to the beautiful harmonies sung by the church choir (made up of students from the attached school and 12 lay vicars).

Follow in the steps of literary greats such as Jonathan Swift and Samuel Beckett and spend a few hours strolling the cobbled walkways or gazing up at the walls of the compact college, waiting for inspiration to strike. Built more than 400 years ago, it’s the oldest university in Ireland.

The Montmartre area of Paris might be more historically linked with lust than love but since the installation of a 40-square-metre monument to love nearly 20 years ago, many lovers now make a pilgrimage to this particular patch of Paris. “I love you” is scrawled across 612 tiles on The Wall of Love in over 300 different languages so no matter where in the world you’re from, this artwork will help you finally say those very important three words.

Stretch your legs on this steep, grassy incline and you’ll discover you’re actually ascending to the top of a volcano – but don’t worry, the last time it erupted was some 340 million years ago so the chance of it bubbling underfoot in the 45 minutes or so it takes you to reach the top is slim. Standing at the peak of this crag is practically a requirement on your first trip to the Scottish capital as it affords some of the best views of the city below and all it will cost you is some sweat.

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