Lausanne, the capital of canton Vaud, can arguably be called the first city of the Alps. As a result is is extremely convenient for some of the best ski resorts in the world.
One of the most convenient resorts is world-class Verbier, which you can get to by road or train via Martigny in just over an hour, taking the gondola at Le Châble up to Les Ruinettes in the heart of the Verbier ski area. Verbier is part of the extensive Four Valleys ski circuit and is famous for its demanding skiing off Mont-Fort and Mont-Gele. It is a ski resort with something for everyone and is also renowned for its apres ski scene.
However there are plenty of alternative destinations. You can take the train via Aigle to Champéry - or drive to Torgon - to have access to the closest major ski area to Lausanne, the huge Portes du Soleil, a perfect ski area for long cruising runs and snow parks. The resorts of les Portes du Soleil are so close that, if you look across the lake in Lausanne, the resorts lie just below the peaks you can see to the south-east. It is also a ski area that crosses into France, allowing you to have lunch in a French resort if you so wish, before skiing back to Switzerland.
German-speaking Zermatt is 3 hours away and is probably better suited for a week or weekend break. It is well worth it though. You can ski across the border to Italy, eat some of the finest food in the Alps and check out the view from the highest ski station in Europe, always in sight of the majestic Matterhorn. Zermatt is a great party town, and still has skiing after every other resort has closed for the season. In fact you can ski there all year round, although summer skiing is very limited. You can find accommodation at Bookings.com.
I have by no means exhausted the options, so for more information either click on the resort names or go to an overview of all Swiss winter sports resorts.