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.

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.

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 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.

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.