We like to grumble, but when it comes to museums, we've got it pretty good in the UK, with free entry to many major museums. In London, for example, it's possible to pop into places like the National Gallery, the British Museum or the Tate on your lunch break without making a dent in your sandwich money. Most museums in Europe do charge an entry fee, but there are still plenty of opportunities for budget travellers to get a free culture fix. Many cities have adopted a free first Sundays scheme, giving visitors access to the permanent collections once a month, while many other museums offer free entry on other days. And of course there are still museums around Europe that offer free entry every day. Some may be small, specialised, or hard to get to – such as the Florence Nightingale Museum in Istanbul – but many, such as the Modern Art Museum in Paris, or the Berardo Collection in Lisbon, are just as grand and comprehensive as their pricier counterparts. Here are 10 free museums across the continent that are worth checking out.

Musée d'Art Moderne de la Ville de Paris

While it may not have quite the je ne sais quoi of the Pompidou Centre, Paris's modern art museum still boasts an enviable collection, with over 9,000 works illustrating all the major art movements of the 20th century. In 2010 five masterpieces by Picasso, Matisse, Braque, Modigliani and Léger were stolen in "the art heist of the century", a haul worth over £80m. The crime was never solved, but the remaining works, displayed in a vast 1930s building with looming pillars, are more than enough for an afternoon wander.
• parismusees.paris.fr/mam, Tues-Sun 10am-6pm, closed Mondays and public holidays

Amsterdam Stadsarchief

Amsterdam's Stadsarchief (city archive), is housed in an imposing, though gritty-looking building, originally the headquarters of an investment bank. Inside, its tiled rooms are decorated with bold, jagged, graphics and patterns. The Treasures of Amsterdam exhibition is a collection of artefacts in the underground Treasury that help tell the story of the city – worth a good nose around while anxiously hoping the heavy vault doors stay open until you're done.
• stadsarchief.amsterdam.nl, Tues-Fri- 10am–5pm, Sat-Sun noon–5pm

Berlin Wall Memorial

While the ghost of the Berlin Wall still lingers around much of the city, this memorial and museum is a fantastic place to learn about the concrete strip that once divided the German capital. The site contains a piece of the wall, with the grounds around it preserved to give a true-to-life impression of the dead space it once occupied – where many who tried to cross were killed by border guards. The visitor centre offers film and books about the wall, while the documentation centre, due to reopen this winter with a viewing platform overlooking the site, includes an overview of events leading up to and following the wall's construction.
• berliner-mauer-gedenkstaette.de. Open-air exhibition and memorial grounds open Mon-Sun 8am-10pm. Visitor Centre open Tues-Sun 9.30am-7pm (6pm November-March)

National Museum, Copenhagen

Charting the history of the Danes since prehistoric times, the National Museum is a proud and comprehensive collection. Particularly interesting is the Stories of Denmark exhibition, which uses thousands of everyday objects to illustrate how life has changed in the country since 1660. It's good for families, with a dedicated children's museum, where the kids can try on period dress and pretend to be Vikings.
• natmus.dk, Tues-Sun 10am-5pm. The children's museum closes at 4.30pm

Berardo Collection Museum, Lisbon

A recent, and impressive, addition to Lisbon's list of cultural attractions, the Berardo Museum opened its collection of modern and contemporary art to the public in 2007. The modern space is filled with vibrant works by all the hard-hitting pop artists, such as Warhol, Pollock and Lichtenstein, as well as greats such as Picasso, Baco and Dali. Regular temporary exhibitions focus on specific artists or themes: there's a wonderful display of vintage posters you simply wish you could own, selected from the museum's unparalleled collection of advertising art.
• museuberardo.pt. Tues-Sun, 10am-7pm

Musée des Beaux-Arts, Nice

Housed inside the striking former mansion of a Ukrainian princess, this museum's building is a spectacle in itself. Once past the iron gates, and through the elegant gardens, you will find an art collection spanning realism, romanticism and symbolism, with works from Monet to Rodin displayed within its palatial rooms. The collection of Raoul Dufy's work in particular is worth a look once you've finished admiring the mansion's gleaming marble interior.
• musee-beaux-arts-nice.org. Tues-Sun 10am-6pm

Museo del Prado

The Prado, one of Madrid's most popular attractions, is simply huge, so it's a real treat that entry is free every evening. There's no need to race through the neoclassical hallways in a futile attempt to see all the sculptures, portraits and murals on display: our advice is to drop in on a couple of evenings and view the rich pickings at your leisure. Highlights include The Annunciation, a lavish gold altarpiece crafted by Fra Angelico in the 15th century, and Peter Paul Rubens' The Three Graces. The museum also offers useful route suggestions for visitors pressed for time.
• museodelprado.es, free entry Mon-Sat 6pm-8pm, Sundays and holidays 5pm-7pm

Florence Nightingale Museum, Istanbul

This is not the most straightforward museum to visit – you've got to arrange an appointment by fax at least 48 hours in advance – but it's worth it for anyone fascinated by the Crimean War and the story of the lady with the lamp. The museum is within the Selimiye Army Barracks, built in 1799, which was the military hospital where Nightingale and her students developed the nursing techniques that saw her go down in medical history. Inside you can explore her personal living quarters, as well as the room that served as an operating theatre. Adding to the experience, which differs from the usual museum fare, is the fact that the guides are usually young soldiers on their military service.
• To arrange a visit, fax the museum on +90 216 553 1009 or +90 216 310 7929 at least 48 hours in advance, stating the date and time of planned visit and including a photocopy of your passport

Museo Storico della Liberazione, Rome

During the second world war, this building in Rome's Via Tasso was taken over by the German security forces, who used it as a headquarters and a base from which to murder and imprison many of the city's civilian population. Once an infamous site of terror, the building is now a museum and the rooms that were once cells for political prisoners are dedicated to the memory of those who were detained.
• viatasso.eu. Tues-Sun 9.30am-12.30pm, Tues, Thur, Fri 3.30pm-7.30pm

Reykjavik Museum of Photography

If you thought the 642 holiday snaps you have on iPhoto were impressive, brace yourself; the Reykjavik Museum of Photography has a collection of around five million photos, dating from 1870. As well as the permanent collection, which also includes objects relating to the art of photography, by contemporary Icelandic photographers.

• ljosmyndasafnreykjavikur.is, Mon–Thurs noon–7pm, Fri noon–8pm, weekends 1pm-5pm