Get ready for a fun immersion in daily life in Budapest— your local guide will show you how to use the metro (one of the oldest in Europe) to easily reach all the city has to offer. Start with a visit to one of the city’s irresistible market halls. Stalls spill over with produce, sausages and meats, festoons of dried paprika, cheeses, and jars of honey, all of it authentically Hungarian. After you leave the market, stop for coffee and a sweet treat at Szamos Gourmet Palace, a combination pastry shop, café and chocolate maker in Vörösmarty Square. Marzipan is a favorite confection in Budapest, and Szamos has specialized in making it since the 1930s, so you might want to try some—but the shop’s truffle selection is equally irresistible. Refreshed, you’ll be ready to hop back on the tram for a visit to the gracious green spaces of Károlyi Garden, sometimes described as Budapest’s most charming small park. You’ll ramble along the boulevards and pass the Hungarian National Museum, truly getting the feel for this dynamic city, as you head back toward the ship.

Your ship sets sail from Budapest after your tour, cruising along the Danube Bend, which is lined with scenic towns—among them are the oldest settlements in the country—nestled at the foot of lovely wooded hills.

Imagine living underneath Budapest for 34 years in a secret abandoned hospital. That’s what one couple did, tending miles of echoing caverns lined with ghostly hospital beds, boxes of files, gas masks . . . gas masks? Yes, gas masks. The Hospital in the Rock began as a hospital during WWII, when Budapest was besieged, but it became a secret nuclear bomb shelter—and hospital/torture chamber for prisoners—during the Soviet era in the 1950s. It was so secret that once it was abandoned in 1970, a single couple continued to live here as caretakers, telling no one what they did. Explore these once-secret caves, seeing 70-year-old hospital equipment still in place, along with some 200 wax figures that stand in for the real people who worked on this site of heroism and horror. Why was this place such a dark secret for so many decades? Can you help unravel its mysteries?

Here’s a fun way to see Vienna: Head to Prater Park. Tweens and teens can zoom around the park on Segways, but there’s plenty for younger travelers to do too, including a ride on the Giant Ferris Wheel, built more than a century ago. Unlike American Ferris wheels, which have open seats, the carriages of the Riesenrad resemble miniature railroad cars. It’s one of the tallest wheels in the world, so you get a fabulous view of the city from the top. Back on the ground, you’ll encounter some mouthwatering classic Viennese sweets—because Vienna loves sweets!—by watching the famous Sacher torte being made at Café Demel, one of the city’s most elegant cafés, and sampling yummy Lilliput chocolates at a shop near St. Stephen’s Cathedral. Younger travelers can get a taste of Habsburg splendor at Schönbrunn Palace. At the Children’s Museum in the palace, girls may dress up in the ruffles and brocades of long ago, and boys can don imperial uniforms. Try on tricorns and powdered wigs, flirt with your fan, figure out how to set the table for an imperial banquet—it’s all fun, but it’s also a glimpse into a long-ago world of protocol and grandeur.

Head outdoors to the beautiful Wachau Valley, one of Austria’s great nature habitats. Hike through vineyards high above the river with a nature expert who will guide you in a hunt for the treasures hiding in this habitat. Can you spot one of the orchid species that only grows here in the Wachau? How about the rare native feather grass? Glimpse a European green lizard basking on a stone terrace or a falcon soaring far overhead, but don’t forget to look out over the river and the valley; these views are so lovely, the memory will stay with you forever.

The skyline of Passau is dominated by two buildings that owe their existence to the prince-bishops who ruled the city until 1803: the great fortress looming on a hill above the three rivers, home to the bishops until the 17th century, and the green onion domes of St. Stephan’s Cathedral. As you walk through the cobblestone streets toward those green onion domes, you’ll realize that Passau retains the layout of the medieval town. However, many of the wooden medieval buildings burned to the ground in the 17th century, and the prince-bishops imported Italian artists to build a new cathedral and a magnificent new residence for the bishops themselves. As a result, these splendid structures flaunt Italian baroque and rococo style and ornamentation, complete with opulent gilding and wonderful frescoes. Your guide will introduce you to some of the architectural highlights—the rococo stairways of the New Residence; the cathedral; and the Town Hall, which boasts a magnificent atrium adorned by large paintings by Ferdinand Wagner—and make sure you get a close-up view of the point where the three rivers meet.

Get into the water this morning: The Ilz River is a great place to paddle a canoe or a kayak—or you could even try some stand-up paddleboarding. It’s splashy fun! Later in the day, you can mount a bike and join a group for a river-hugging ride that starts at the bike ferry across the Danube. You’ll pedal through the lovely countryside between Engelhartszell and Passau—orchards and meadows glide past, along with the occasional castle, charming village or picturesque ruin. Your expert bike guide will have a surprise waiting for you somewhere along the route, too!

Here is your opportunity to see German engineering, famous the world over, in operation as you tour the state-of-the-art BMW factory on the outskirts of Regensburg. About a thousand cars a day roll off the assembly line here, many of them in the BMW 3 series. You’ll see the fascinating production process from beginning to end, starting with rolls of sheet metal that are stamped out into body parts and continuing as the body is built and the various other elements are robotically assembled. You’ll follow a car into the finishing department to see it painted, polished and have the final touch applied—the BMW roundel.

Don your safety goggles and discover how BMW builds a thousand cars a day at their Regensburg plant. Robots and humans work together to assemble a single car—which has about 550 parts—in less than 40 hours (it used to take weeks). The place is huge, and though robots do a lot of the work, a great deal still needs to be done by the human hand. You get to see all aspects of the process, from stamping out metal parts to painting, in a tour tailored to young visitors.

If you’d rather see some of historic Regensburg, you can experience it from the viewpoint of its modern-day teenagers, who will show you where to shop, stop for a bite to eat at a thousand-year-old sausage stand and find the best ice cream. They’ll also point out all the must-see sights—the cathedral, the medieval bridge and the house where Oskar Schindler lived.