GETTING THERE: The Valais is visited by skiers in the winter and early spring, Swiss and German vacationers in the summer, and hardly anyone in the fall. Cars arrive in the valley from eastern Switzerland by way of the Furka Tunnel or Pass, from Italy by way of the Simplon Tunnel or Pass, from southern France by the Great St. Bernard Tunnel or Pass, and from northern Switzerland and France by way of Lake Geneva. The nearest major airports are in Geneva (about a 50-mile drive), Zurich (75 miles) and Milan (100 miles).
The Glacier Express train, which runs along a spectacular route from St. Moritz in eastern Switzerland to Zermatt in the Valais by way of Andermatt and Brig, runs all year. There are also more conventional trains that parallel the Rhone.
GETTING AROUND: The logical way to explore the Valais is to follow the Rhone. The river bisects the province; from the towns along it, roads branch off to the lateral valleys to both the north and the south.
Driving these rougher routes can be tricky, as the roads zig and zag along the mountainsides, and everyone appears to be in a mad rush to get to Zurich by lunch time. But when it's not snowing -- which admittedly isn't often; in the mountains the first snow can arrive the second week of October and stay until June -- and as long as you have minimal confidence and competence behind the wheel, you won't have any problems. The Swiss are among the world's best engineers, and build their roads and bridges with precision. If your nerve fails, the yellow postal buses go everywhere.
WHERE TO STAY: Even in the off-season, the Valais, like all of Switzerland, is not particularly cheap. Hotel rates range from $30 for a double without bath in the more remote villages to two and three times that in the resorts of Montana and Crans.
For those who wish to follow in Katherine Mansfield's footsteps and stay in her room in the Chalet des Sapins, the Hotel Helvetia (3962 Montana-Vermala, Valais, Switzerland, phone 027-41-21-77), which owns the chalet, closes for a month each spring and fall. Reservations are advised.
WHERE TO EAT: While none of the restaurants in the Valais is outstanding enough to warrant a trip in itself, most offer solid, unpretentious Swiss food. Valaisian specialties include raclette, where a half-wheel of local cheese is placed in front of an open fire. When it begins to melt it is scraped off onto a plate and eaten with small potatoes and pickles. Other specialties are cheese fondue and bundnerfleisch -- smoked and dried beef that has been cut into very thin slices.
EXCURSIONS: The Valais is known for its skiing, hiking and walking. Among the most popular winter sports resorts are Zermatt, Grachen, Saas-Fee, Champery, Verbier, Riederalp, Montana and Crans.
From any of the villages in the lateral valleys there are paths up into the mountains suitable for a day's jaunt. More experienced hikers have numerous routes open to them.
Two other popular -- if wildly different -- activities are hang gliding and following the vineyard route from Martigny to Sierre.
For those in search of Rilke, there has been a recent spate of translations and books about him in the past few years, all leading up to the 50th anniversary of his death next year. The best selection of the poet's work is in Stephen Mitchell's wonderful translations, especially his "Selected Poetry" (Vintage). The Hotel Bellevue in Sierre, where friends stayed when they visited Rilke, is now part of the city hall. A second-floor room, le salon bleu, has been set aside as a museum in the poet's memory.
INFORMATION: Swiss National Tourist Office, 608 Fifth Ave., New York, N.Y. 10020, (212) 757-5944.