Public bathing spots on a river that runs through the middle of a financial capital, a Dada bar still trading, and honest numbers on the prices.

Eighty-five per cent of the city was deliberately destroyed and then rebuilt from paintings. What to see, and why the Palace of Culture divides everyone.

The Staatsoper sells standing places for a few euro on the night. Around that queue, a Vienna day runs from the cathedral roof to the Naschmarkt and a coffee house that will not hurry you.

Venice now charges some day visitors to enter, and the cheapest gondola ride in the city costs two euro and lasts three minutes. What a single day here should actually contain.

The old town survived the twentieth century almost whole. Then walk twenty minutes north and see what the other half of the century left behind.

Gamla Stan takes ninety minutes and then you should leave. The ship museum, the underground art and the island the locals actually use are elsewhere.

A cathedral tower with no steps, a palace still used by the royal family, and a heat schedule that decides everything from June to September.

A single day in Rome works if the Colosseum slot and the Borghese booking are settled before you arrive. Here is the walking order that follows from those two fixed points.

Geothermal water, a concert hall made of glass honeycomb, and the northern lights question answered honestly. One day in the northernmost capital.

Charles Bridge before eight is a different bridge. A Prague day built downhill from the castle, with the tram that does the climbing and the currency law that gets your money back.

Cross the bridge to taste port, pay five euros to enter a bookshop, and eat a sandwich covered in melted cheese and gravy. One day on both banks of the Douro.

The Viking ships, the Fram, the sculpture park that is free at all hours, and an honest warning about what things cost here.

A standing wave in the middle of a city park, a law that lets you bring your own food to a beer garden, and one very overrated glockenspiel.

Fifteen minutes with a fading fresco, if you booked in February. What to do with the rest of the day in a city that is not trying to be Rome.

Free evening entry to the Prado and the Reina Sofia changes the shape of a Madrid day. Here is how to use it, when to eat, and why the covered market by Plaza Mayor is not where locals go.

Tram 28 is a pickpocket’s commute and the Santa Justa lift has a back door that costs nothing. A Lisbon day through Alfama, Belem and the custard tart queue that moves fastest.

The bugler breaks off in the middle of a phrase, every hour, for a reason from 1241. Plus the market square, the Jewish quarter, and what to do about Auschwitz.

The public ferry across the Bosphorus costs the same as a city bus and does what the cruises charge thirty times more for. One day in Istanbul, from Hagia Sophia to a fish sandwich at Eminonu.

Ferry out to an island fortress, sit in a public sauna with strangers, and see a church blasted out of granite. What one day here actually holds.

Two closed Mondays, 463 steps with no way out halfway, and a five-day cathedral ticket that most visitors use for an hour. Planning one day in Florence around what is actually open.

A one o’clock gun, a street built on top of another street, and a free gallery most visitors walk past. One day in Edinburgh, with a warning about August.

Two kilometres of city wall, no shade, and up to four cruise ships in the harbour. Timing is the whole trick here.

Trinity’s Long Room has been emptied of its books for conservation, which changes what the ticket buys. A Dublin day through Georgian doors, a working pub at five, and the jail that made the state.

The statue everyone photographs takes four minutes and disappoints. Here is what the rest of the day should be, on two wheels.

Szechenyi opens at six and is nearly empty until nine. A Budapest day that starts in hot water, crosses to Buda for the hill, and ends in a courtyard bar that was condemned property.

Manneken Pis will disappoint you in under a minute. The Grand Place, the comic murals, the beer list and the chips will not.

A double row of cobbles marks where the Berlin Wall stood, and following it explains the city faster than any museum. One day, from the Reichstag dome to the East Side Gallery.

The Sagrada Familia and Park Guell both sell timed entry online and both refuse latecomers. Around those two windows a Barcelona day builds itself, from the Boqueria to the Carmel bunkers at sunset.

The combined archaeological ticket includes the Acropolis and six other sites for five days, and the booths rarely mention it. An Athens day from the marble at dawn to a rooftop looking back at it.

The Anne Frank House has no ticket desk and releases seats six weeks out. Plan a day in Amsterdam around that release, and the canals, the Rijksmuseum and De Pijp fall into place behind it.

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