Martigny is an elegant town of around 20,000 people, located in the Rhone valley at the point where the river swings from an East-West direction to South-North. The valley of the Dranse also runs into Martigny, and it is alongside this valley that the trains run to La Châble and connect to trains for Orsières. Additionally trains run to Chamonix in France via Les Marécottes and Le Chatelard. The town is in the heart of a significant wine-growing region, has several museums, some Roman ruins and lies beneath the imposing La Bâtiaz Castle. There is plenty to keep you occupied in town, but if there is snow on the mountains and clear skies, there are few better bases to get to a number of significant ski and snowboard areas.
Amongst the ski areas you can easily reach are Verbier, Bruson, Ovrannaz and Les Marécottes. The resorts of Les Portes du Soleil are also an easy outing, via Aigle, and - with a change to a bus at Sion - a large number of other resorts in the Valais can be reached.
There are excellent rail and road links to Martigny from Geneva Airport and Lausanne. The station is a stop on the main line between Geneva, Lausanne, Brig, Visp and Milan, and a motorway passes within a kilometre of the town.
Martigny has a good range of hotels, although sadly no backpacker hostel. I like to stay in the 3-star Forclaz-Touring since it is only a short walk from the station, is central for the town centre and has fast, free wifi. It's a bit dated, but the rooms are clean and pleasant.