'Nowhere more stuffed full of art and art history': Klim's Ondine silver fish on the Danube. Photo / Getty Images
It starts with Sisi. The Habsburg's very own Queen Elisabeth, known as Empress Sisi, a German in the Austrian court who hated Vienna — all those palatial lumps of stone, the endless formalities — and escaped when she could.
Rode the railroad, her Imperator Express, into the flat plains of Hungary, to her beloved summer palace at Godollo and freedom in the forest.
Godollo is the charming version of baroque: big windows, intimately-scaled rooms, a sense of wealth but not overwhelming ostentation. And the train that takes you there on an APT tour is Sisi's own, restored to all the glamour of the original: the woodwork, brass and brocades, the velvet drapes and Persian carpets.
She wasn't really slumming it in Godollo. Nine kitchens. A thousand servants, probably half of whom were woodcutters keeping the fires going so the rooms stayed warm.
She and her husband, Franz Joseph, were almost the last Habsburg rulers in a dynasty that stretched back 640 years. He was brutal in suppressing the Hungarian revolution of 1848 but he could not hold back reform forever. In 1867, with Sisi's encouragement, he cut a deal known as "The Compromise".
It was a bit like the Treaty of Waitangi, really: as king of Austria he would become emperor of Austria-Hungary and in return he would guarantee to respect the rule of their laws.
"You can't ride two horses with one bottom," they said at the time.
Sisi was beloved but she had issues. Ate almost nothing in public, rode horses and walked for hours every day. She weighed less than 50kg and her hair reached nearly to the floor.
In every portrait she looks the same: a beautiful, impossibly thin 30-year-old woman. She allowed no official photographs and no painter could show her older. There's a family portrait in the Godollo, painted shortly before she died, aged 60: she still looks 30 and is surrounded by retainers who look much older, although they were her own age. Even her own daughter looks far older.
"Body image disorder" is the phrase the guides use today. She had herself laced so tightly into leather corsets that her waist was a mere 40cm. When she died, stabbed by an Italian anarchist, she didn't feel the shank go in and no blood spilled out. She felt faint.
"What has happened to me?" she asked, confused. They loosened her corset to find out, and she bled to death.
Hungary. Where they speak a language unlike any other, and more complicated. Why say cheers when you can invent a word like "egeszsegedre"? They gave the world goulash and have 40 names for the paprika that flavours it. They invented the light cavalry — huzzah for the Huszars, dashingly buttoned into their tunics, moustaches atwirl and swords gleaming.
On the APT excursion, they greet you at Godollo with Huszars on horseback and a brass fanfare, the horses skittish on the uneven flagstones.
It's splendid on the boat. Cruising upriver on a sunny afternoon, past little beaches, big Ursli-style houses up in the hills, the forest down to the water, medieval battlements growing atop the bluffs. Cyclists glide along the embankments, there are church spires in all the tiny villages, sometimes half a dozen at a time.
A great sense of cultural confidence and a beauty that derives from it. Old stones, settled communities, geraniums in every window box.
On the boat they feed you handsomely with an endless parade of buffets and a la carte meals. Smoked trout for breakfast, if you want, but you can get your granola and bacon and eggs too.
There's also a heavily ritualised procession of events: the welcome, special briefings, visits to the captain's table, the last night. The captain and his senior staff tell their jokes, the bartender tells you later to forget about them, he is the most important person on the boat.
And every day, the enormous pleasure of visiting a new city and returning each evening to the same room. You unpack and pack up again just once, and yet you visit half of Europe.
Vienna. Is there a city in the world more stuffed full of art and history?
Sisi is important here, too. It's where she lived, after all, but while Hungarians want you to know her heart was with them, in the Austrian version of her story Hungary isn't mentioned at all.
They're also big on Maria Theresa, empress in the 18th century. In the long history of the Habsburgs, through the Holy Roman Empire and then the Austro-Hungarian Empire, she is the only woman to have ruled in her own right.
She does rather put ordinary mortals like Jacinda Ardern in her place. Maria Theresa ran the government, conducted endless wars, defended religious tolerance and had 13 children who survived and three more who didn't. The 13 included Marie Antoinette, who survived until she didn't.
There's a big family portrait in the Schonbrunn Palace, painted when they'd got to 11 children. They're identical, although different ages: every girl and boy has exactly the same face. Painters had such a hard time.
In the portrait her husband, Francis, is pointing casually at her. She's the one, he's saying, his message reinforced by a couple of dogs, the bitch in obeisant posture to the empress while her mate, like Francis, points an obedient paw at his queen.
The Schonbrunn was their summer house. It's vast, with the obligatory wasteland out the front, where once the troops endlessly paraded, and there are enormous formal gardens out the back, rising up a long grassed slope to a "coffee house" that looks bigger than Buckingham Palace.
Always, the old is the context for the not so old. Mozart performed at the Schonbrunn as a 6-year-old and afterwards — they admit this may be untrue — told Marie Antoinette he wanted to marry her; John F Kennedy sat down there with Nikita Khrushchev in 1961, in the first summit of the Cold War.
Vienna is a monument to wealth and power. In the middle of town the chambers of the Hofburg Palace drip with bright, shining gilt. The cathedral of St Stephen manages to be both gloomy and gilt-ridden and is clearly intended to frighten people; the State Opera, bombed but not destroyed during the war, is lighter and more graceful.
Horses in pairs draw carriages around the cobbled lanes, most with two or three taxis crawling in their wake as if they too are being towed along.
"You see that statue there?" said our guide, standing in the shopping mecca of Kartnerstrasse. It was old Archduke Karl, with a chin that protruded well past his nose. "It's been photoshopped. In reality the chin was worse."
Six hundred years of intermarriage took its toll on the Habsburgs and it wasn't just the family chin. They had a great deal of mental illness. Perhaps it became self-perpetuating: if you were born into the maddest family in Europe, wouldn't you feel obliged to go at least a little troppo yourself?
Surprisingly, given the inherent conservatism of Viennese traditions, the artist they celebrate the most is the intricately decorative and erotically obsessed Gustav Klimt. From the loftiest art museums to the kitschiest tourist shops, his painting The Kiss is everywhere.
Perhaps that's fair enough: it's far more engaging than, say, Rodin's The Thinker or Munch's The Scream. I got my Kiss in a snow globe.
Durnstein packs the entire rural Danube into one tiny place. A very pretty monastery in a village entirely devoted to selling souvenirs and, high on the hill, the ruined castle where Richard the Lionheart was imprisoned on his way home from the Crusades.
This is the start of the Wachau Valley, the section of the Danube that inspired Johann Strauss to write The Blue Danube. Which is green, it's never been blue, it's a little German joke although no one really seems to know what it's about.
The river valley is perfect for bike riding. It's a ravine, in parts, and on the steep slopes above you are vineyards on terraces held up by stone walls 600 years old.
At the other end of the valley is Stift Melk, an enormous abbey of the Counter Reformation: a bleak and bluntly massive baroque edifice towering over the town, designed for bishop-princes to show those Lutheran peasant ingrates who was really in charge.
There is much overblown art in the chapels, and in the concert hall they have a ceiling fresco with perspectives that only make sense if you sit exactly in the royal spot. Maria Theresa did come, once. "I would regret if I had not been here," she said. Which does sound like faint praise.
Back on the boat, sitting on the top deck as evening falls in the valley, it remains with you. And tomorrow you will be in Germany.
1. Much of the travelling is by night, so when you can during the day, make time to sit on the top deck. It's lovely, watching the world glide by.
2. Don't leave all the planning to them. Go online to see what exhibitions and events are on while you're in town, so you can use your free time well.
3. For that free time, ride a bicycle. All the tour boats have them. The towns are flat, with bike lanes and gentle traffic, and you can see so much more than if you're walking, be so much closer than if you're on a bus.
4. Eat local: Try the local dishes they serve on board and, when you can, eat at local cafes and restaurants too.
5. Get the guides talking. They're generally well informed and insightful and only too pleased to talk.
Telegraph: “A bingo card of disappointments.”