Open-air cafes line the riverbanks, and locals mingle with tourists to engage in earnest conversation or to take coffee, relax, sit in the sun and feed bread scraps to the fat but ever-hungry ducks and swans. These must be the best-fed birds in Europe. In the distance beyond the last bridge, the river widens into a lake where steamers sporting black funnels, yellow deck chairs and a spick-and-span white superstructure glide serenely across the sparkling water.

This is Lucerne.

Looking up to the snow-covered peaks that circle this town, I can see why Switzerland is such a magnet for people who love mountains. Lush green meadows with a freshly mown look rise, first slowly, and then more steeply. The majestic firs and pines that are abundant at lakeside level thin out, then disappear higher up as the white-capped pinnacles soar into the sky.

We are staying at the magnificent Palace Hotel, one of the classically Swiss, turn-of-the-(last)-century grand hotels I find so attractive. Its position right on the lake, the friendly staff, the excellent service and fine meals make our stay here a delight. I turn to the concierge for advice on what to see and where to go.

“Start at the lake,” he says. “The steamers run every 20 minutes and I would advise you to take the lake trip. You can get off at any of the points where cable cars will take you to the mountaintops.”

We board the steamer, which leaves from the landing right opposite the railway station. We have decided to visit the Rigi by taking the lake boat to Weggis, then connecting with the cable car to Rigi Kaltbad. This links with the Vitznau train to the top so we can get to Mount Rigi one way and go home the other.

“Unless you are young and extremely fit, you may prefer to walk down the mountain rather than climb up,” the concierge advised. “To get to Mount Pilatus, board the red train at Alpnachstad for the ride up the mountain, then descend by cable car via Fraekmuentegg.”

The cogwheel railway, reputedly the steepest in the world, climbs steadily through cloud-filled valleys, passing grazing cows reminiscent of those featured in dairy and creamery advertisements. Contentedly munching on grass as the bells around their necks sway to peal out a cacophonous offbeat carillon, they barely take notice of the passing train.

Higher and steeper chugs the rain, climbing first through the tree ine and eventually past all vegetation as it strains its way to the viewing platform, hotel and daredevil skislope at the very top. Here, in the thin, crisp mountain air, we sip steaming coffee and soak in the view before dangling our way back to Lucerne on a spine-tingling gondola ride, our cable car suspended in space high over the valleys below.

The next day is beautiful and sunny, ideal for more exploring. We head for Vitznau, taking the long and strenuous walk to the peak. It is worth it. The alpine panorama is absolutely magnificent. On this glorious, clear day we are able to see almost 200 miles in each direction.

Another memorable day trip takes us to Burgenstock, also reached by steamer and cog railway. Home to about 100,000 inhabitants, the town relies on tourism as a major source of income. Residents are friendly and welcoming.

Here, too, we feel that we are on the roof of the world. We particularly enjoy the wonderful, wildflower-edged walking path that is cut 1,500 feet above Lake Lucerne. Not too strenuous, it finishes at a vertical elevator that seems to be precariously balanced on the mountainside but is, in fact, ultramodern and safe. At the top we find a wonderful Swiss country-style restaurant. The classic views of meadows and forests present the very best in postcard-perfect scenery. Crisp mountain air, bell-necklaced cows, a delicious lunch of classic Swiss veal and roesti (grated potato fried to a golden brown) and a walk back down through steep pine-forest paths make for a perfect day.

By now we fully rely on the guidance of ou r wise concierge. His next suggestion: “You must look through the town. It was the favorite of Goethe, Victor Hugo, Queen Victoria and Mark Twain. There is such a variety of interesting sightseeing that you could spend two weeks without going back to the same spot twice.”

We follow his advice and spend a day in Lucerne just wandering around the Altstadt (Old Town) — one of the world’s best-preserved medieval cities, it is extremely atmospheric. We walk to the Weinmarkt and the watchtowers that mark the city walls, then settle to watch the parade of humanity as we enjoy coffee and a piece of marvelously calorie-laden Swiss pastry in one of the many riverbank cafes.

Our next outing is to the medievallooking fairy-tale castle Chateau Gutsch. Following a steep cable-car ride from the town that it so majestically overlooks, we have lunch on the balcony, with its splendid panoramic view of Lucerne, the lake and distant Alps. Inside the castle-like hotel we find all the trappings of antiquity — centuries-old wooden ceiling beams, splendid suits of armor, antique paintings and tapestries. A local friend tells us that the whole castle is a replica — Lucerne’s own version of a Disneyland-esque fantasy.

We need balance, and so console ourselves by taking the hour-long train ride to the picturesque Benedictine monastery of Engelberg. Founded in 1120, this is the real thing. Its library contains illuminated manuscripts dating back nearly 1,000 years.

Lucerne is a place for exploring, enjoying and discovering, but the method of your journey is up to you. Set out to experience the many varied destinations around the lake or settle in to wander the wonderful little streets of Old Town. Either way, you’re in for an adventure.