Get lost in infinity or dance on the ceiling at the museum of immersive optical illusions. One of Zürich's zaniest attractions, the WOW Museum will appeal to kids of all ages (and adults young at heart). 

Spend some time wandering round Zürich's old town, along the historic streets of Rennweg and Augustinergasse, home to pretty buildings, shops and cafés, or walk to Lindenhof for views over the river and city. Visit the Fraumünster, a former abbey famous for its stained glass windows, then finish off with a visit to Café & Conditorei 1842 for a hot chocolate (or tipple) and cake in elegant surroundings. 

Pay a visit to a football-lover's heaven, the FIFA World Football Museum. Even those who are less than mad about the beautiful game will find plenty to keep them entertained among the interactive exhibits and events.

Experience one of the city's romkocsma, or 'ruin bars', dilapidated old buildings that have been turned into bars featuring upcycled furniture. Szimpla Kert is the oldest and most famous, with live music a few nights a week, and a flea market during Sunday daytime.

Looming over Budapest, the 19th-century lookout tower of Fisherman's Bastion gives the best views of the city. If the walk up to the top of the hill on which it sits is too daunting, just hire an electric scooter to get you there – Budapest has plenty of companies renting them out.

A must-visit in Budapest, Szent István-bazilik (St Stephen's Basilica) is a Neo-Classical delight complete with vibrant stained glass, towering dome and sumptuous marble decoration. Some tickets include entry to the treasury, plus a terrace on the outside of the cupola – the highest lookout point in Pest.

Don your walking boots for the steep hike up Muntele Tampa (Mount Tampa), part of the Postavarul Massif that sits 400m above the city that surrounds it. Once you're at the top, there are a variety of walks to embark on. If you'd prefer a more relaxed journey, there's a cable car to take you up the mountain in a matter of minutes. 

Visit the Black Church (Biserica Neagra), an impressive Gothic church with a rich history that is over 600-years old and is named after it's blackened walls from a 1689 fire. 

Visit the world's third-largest administrative building, the Palatul Parlamentului (or Parliament Palace), built at the request of Nicolae Ceausescu and formerly known as the People's Palace. It is built, furnished and decorated exclusively with Romanian materials. Take a guided tour to explore the opulent interiors, grand halls, and learn about the history of this colossal structure.

Learn about traditional Romanian rural life at the Dimitrie Gusti National Village Museum, a collection of vernacular buildings by Herăstrău Lake. Wander through the open-air museum to see homes, churches and workshops from the last four centuries.

Explore Bucharest’s 45-acre Botanical Garden. Highlights include the gently crumbling Old Greenhouse, the rose garden, and the Botanical Museum. The lawns and lakeshore are popular picnic spots on sunny days.

Vienna's Jewish Museum honours the thousands of Austrian Jews killed in the Holocaust, and also celebrates the history and ongoing cultural contributions of the city's Jewish community. The museum also offers themed tours from time to time – book ahead if you'd like to join one.

Vienna's Imperial Palace, The Hofburg was the former residence of the Habsburg dynasty. It has grown over the years to become an impressive complex of museums, churches and gardens. The Sisi Museum, Imperial Treasury and Imperial Apartments offer a glimpse into the lavish lifestyles of the emperors, and the famous Spanish Riding School and the Austrian National Library are also located on the complex. 

After seeing the highlights, get some fresh air in the Burggarten and Volksgarten or explore the alleyways filled with pretty churches and coffee houses. 

Pay a visit to the Schönbrunn Palace. The Habsburg’s residence’s huge size has to be seen to be believed; the building contains over 1440 rooms! The adjoining classical gardens are just as impressive.

Take a dip in one of Europe's most stunningly restored swimming pools, the Müllersches Volksbad. The building has an Art Nouveau dome and the steam rooms are full of Baroque touches like murals, stucco, bronze statues and ornate iron bars.

You could spend hours at the Pinakothek der Moderne discovering works from the most famous art movements. All the big names of modern art – Kirchner, Kandinsky, Klee, Bacon, Braque, Otto Dix, Picasso, Magritte, Ernst, Miró – are present in the museum's impressive permanent collection.

Explore the Munich Residenz, home to Bavarian dukes, electors and kings until 1918. Spend some time getting lost in the fascinating museum or the perfectly manicured gardens.

Visit the shop of Patrick Roger, the famous Parisian chocolatier, who takes the art of chocolate to another level. Marvel at his sculptural creations and taste some of France’s most unusually flavoured and exquisitely crafted chocolate.

You'll find Europe's largest collection of modern and contemporary art at the Centre Pompidou (or Beaubourg as it's often called), housed in a striking building covered in pipes and scaffolding. Inside, you'll find temporary exhibitions alongside the permanent collection that includes masterpieces like Duchamp's Fountain, and recognisable works by Frida Kahlo, Robert Delaunay and Wassily Kandinsky.

Head to Paris' Marais quarter for indie boutiques and some of the city's coolest bars.