Six days in the Swiss Alps: Zermatt to St. Moritz, and eight hours of train in between

The train from Visp takes about eighty minutes up a narrowing valley and stops in the middle of the village, where an electric buggy from your hotel will probably be waiting. There are no cars to dodge on the walk out of the station, which takes a few minutes to get used to.

Spend the afternoon on foot. The village is three streets along the Vispa with lanes of old timber granaries standing on stone discs between them, put there to keep the mice out of the grain. At the southern end the street opens and there it is: a four-sided pyramid, on its own, at the head of the valley.

It was one of the last big Alpine peaks to be climbed, in 1865, and the first party to reach the top lost four of its seven men on the way down. The mountain is on the label of every chocolate bar in the country, and it still stops people mid-sentence.

Eat somewhere unambitious and Swiss. Fondue, raclette, a carafe of Valais white, and an early night, because tomorrow starts high.

Take the first rack railway of the day. The line leaves from opposite the main station and grinds up to a bare ridge above three thousand metres in about forty minutes, and the view from the top is the one people come to Switzerland for: the Matterhorn on one side, and on the other a glacier running down between a horseshoe of four-thousand-metre peaks. Go early, both for the light and because the first two trains are half empty.

You can walk back down as far as you like and pick up the train again at any of the stations on the way, which is much the best way to do it. An hour of downhill path buys you the same view without the window in front of it.

In the afternoon take the cable cars up the other side to the Klein Matterhorn, at 3,883 metres the highest station of its kind on the continent. There is a glacier palace cut into the ice, a viewing platform reached by a lift through the rock, and skiing in July. It is cold, thin-aired and unlike anywhere else in this trip.

From the same station a roped party can walk up the Breithorn in a couple of hours. It is the gentlest of the four-thousanders and still a glacier climb: crampons, rope, guide. Several schools in the village take beginners up it, and it is worth asking about if the idea appeals.

Today is the train. It leaves Zermatt in the morning and reaches St. Moritz in the early evening, roughly eight hours to cross the country sideways, and there is nothing to do but sit in a panoramic carriage and watch the Alps change character three times.

The first stretch runs back down the valley and up the Rhône, mostly pasture and vineyards. Then it climbs the Oberalp pass at just over two thousand metres, which in early summer is still walled with snow, and drops into the Rhine gorge, a canyon of white limestone that Switzerland calls its own Grand Canyon. The last stretch is the best: the Albula line, a piece of nineteenth-century engineering that spirals through the mountainside in tunnels to gain height, and a world heritage site in its own right.

Lunch comes to your seat if you order it. The wine glasses have slanted stems, which is a joke about the gradients and a genuinely good souvenir.

You arrive with enough evening left to walk into St. Moritz and eat. The oldest building in the village, a farmhouse of 1658 with painted walls, has been a restaurant and bar for a century, and it is the right place to celebrate having sat down for eight hours.

Start with the classic Engadine view. A short train ride down the valley and a red funicular built at the start of the last century lift you to a terrace at about two and a half thousand metres, and from the restaurant balcony the valley runs away below you with its four lakes in a line, the whole thing bent slightly, like something drawn rather than found.

There is an easy path along the hillside from here, roughly level, that most people can walk for an hour or two before turning back or dropping down to a station. Take it. This is one of the few places in the high Alps where the good view lasts the whole walk instead of arriving at the end.

In the afternoon, back in St. Moritz, the Segantini Museum is a small stone rotunda built in 1908 for the painter Giovanni Segantini, who spent his last years in these valleys painting the light you have just been standing in. His unfinished triptych of Alpine life fills the upper room. It takes half an hour and it changes what you saw in the morning.

Finish with the leaning tower on the way back to dinner, a twelfth-century survivor of a church that was demolished around it and now tilts, visibly, opposite the grandest hotel in town.

The Bernina line runs south from St. Moritz towards Italy and is the higher and wilder of the two railways here. Twenty minutes down it, a cable car climbs from a lonely station to Diavolezza, just under three thousand metres, and puts you on a rock terrace directly opposite a wall of ice.

What you are looking at is the north side of the Bernina massif: hanging glaciers, seracs, and the striped face of Piz Palü, which is one of the great sights of the Alps and, unusually, requires nothing of you but the price of a ticket.

For walkers, the ridge above the station gives a half-day circuit with the glaciers below you the whole way; allow four to five hours, take water, and check at the top station whether the path is clear of snow, because it often is not until July.

Come back down in the late afternoon and eat in the village rather than at a hotel: there are a couple of plain, good Engadine restaurants away from the lakefront, and they cost a third of what the terraces charge.

Keep the last morning short. Walk the lake shore below the village, which is flat, quiet and the one place in St. Moritz that does not try to sell you anything, and take in Chesa Futura on the way back: a curved timber building on stilts by Norman Foster, clad in larch shingles that have weathered to grey, and either the best or the worst building in the Engadine depending on who you ask.

Then the train. The line to Chur takes two hours and includes the spirals and viaducts of the Albula, which you will have come up in the dark half of yesterday's light if you arrived late, and it is worth the window seat again.

From Chur, Zurich is another hour and a quarter, and the airport is on the same train.