Arthur Tauck had a grand idea: to offer a guided trip which was truly all-inclusive. His first all-American coach tour took travellers around New’ England in this revolutionary style. That was 90 years ago, and his model has been much imitated since. Now, Tauek’s global offering includes river cruises in Europe – one of the most fascinating being a 12-day voyage along the Danube. What sets Tiuek apart is its exclusive access to several stunning palaces, the first of which is the family-owned 16th-century Lobkowicz Palace in Prague, where we begin with a fascinating dinner (the palace was confiscated then returned to the family after the fall of communism) before joining the riverboat in Germany’s ‘sausage town’ Regensburg. MS Savor is a slick operation: just 67 cabins, all contemporary, spacious, and designed to make the most of the light. We lounge on the sundeck, with its putting green and hot tub, as we sail across the borders of five countries.

The Wachau Valley is an absurdly pretty part of the journey, a green, green stretch where Christmas trees surround fairytale castles built high on promontories which are both formidable and bewitching. Apricots grown here are as fat as figs and sweet as dates – and we fill our boots and bags with jam, oil and schnapps.

The beauty of the itinerary is that we sail through the less exciting destinations at night and stop to explore the must-sees. Day trips are always with local guides who tell us what it was really like to live through communism and take us to the coolest cafes. We pause often for treats such as gingerbread and plum brandy. Cesky Krumlov is a colourful chocolate-box of a town, off-radar to most visitors in the Czech Republic thanks to its hard-to-get-to location. We arrive in plenty of time to visit its baroque castle before what small crowd there is does surface.

We’re an energetic bunch (mostly Americans), from the 30-something solo traveller to the 92-year-old racing ahead. One day we take bicycles out for a ride through Durnstein’s vineyards for Dinners in the formal Compass Rose Dining Room showcase the best of each country we pass through: feasts of Bavarian sausage and beer, goulash paired with Hungarian wine and a mountain of Viennese desserts. We can, if we want, work it all off in the gym – but not one of us does.

The most magnificent evening of all, is spent at the Palais Pallavieini in Vienna, where ballet and opera performances punctuate an epic supper in what is truly the city’s most opulent dining room. We disembark in Budapest, where we stay at the fabulous Four Seasons Hotel Gresham Palace and our enthusiastic guide takes us to food markets, the funkiest church I’ve ever seen and, yes, even the city’s ruin bars. A fitting street-savvy flipside to the private views before.