1. Amsterdam – enjoy a free musical performance

Formed in 1974 in an old furniture showroom near the red-light district, the Bimhuis was set up by a bunch of jazz musicians keen to ditch the old and embrace the new.  This emphasis on improvisation and workshopping continues to this day, and after their Tuesday night practice, the musicians stay on to perform to an audience. There’s no need for a ticket, just show up with a keen ear and an open mind.

2. Copenhagen – free bicycle rental

The folks behind Copenhagen Free Bike Rental have one goal – to get as many residents and visitors to the Danish capital out of their cars and onto two wheels.  This non-profit organisation rescues rusty and salvaged bicycles, fixes them up and, if you meet them at Trianglen square in Østerbro, will loan you one for the day.  All you have to do is promise to bring it back and, if you are able, make a donation to their organisation in money or in kind.

3. London – visit a museum

Many of London’s museums are free of charge but two in particular give tourists an insight into the city itself.  The Museum of London Docklands explores the story of how the derelict docks and rusting cranes of the Thames to the east of the city have been transformed into luxury housing and a prosperous financial district.  Over at the Barbican, its sister museum the Museum of London documents the growth of London from Roman times.

4. Rome – take a free guided tour

Unravelling Rome’s mysteries and understanding its long history is a lot easier with a guide, so take a walk with New Rome Free Tour.  A licensed guide meets visitors every day at 5.30 at the foot of the Spanish Steps to show them some of the city’s most famous sights, including the Pantheon and the Trevi Fountain.  Use the money you save to throw a coin into the fountain – it’s said to ensure your return to the Eternal City – but don’t forget to tip your guide if they’ve done a good job.

5.  Paris – pay your respects to some of history’s most famous characters

The remains of some of history’s most well-known names are interred in the cemeteries of Paris, the largest being the Cimetière de Père Lachaise.  Take the Metro (Line 3) to Gambetta station; as you enter the cemetery you’ll see the grave of Oscar Wilde.  From there it’s downhill to the rest of the cemetery, where you’ll be able to pay your respects to historic figures as diverse as Jim Morrison and Edith Piaf, Bizet and Chopin, Proust and Balzac.  Pick up a free map to make sure you don’t miss anyone important.