Geneva: A great option because of the choice of flights from the UK, and the number of resorts that are nearby. These include Chamonix, Courmayeur, Flaine, Morzine, Samoens, Morillon, Avoriaz, and Megève (all of which are less than 90 minutes' drive). Swiss resorts such as Verbier can be reached from here too, although the commute is slightly longer.
Grenoble: Good for Alpe d'Huez, Les Deux Alpes and Serre Chevalier. At a pinch, you can also use it to get over to the resorts of the Tarentaise in France (for example, Les Arcs, La Plagne, Meribel, Courchevel and Val Thorens), although the transfer times are longer.
Chambery: Provides the best access for the famous resorts of the Tarentaise in France, for example Les Arcs, La Plagne, Meribel, Courchevel and Val Thorens (although it's more susceptible to fog). You might struggle to find accommodation for just a weekend in these perennially popular destinations.
Turin: Good for Sestriere, Sauze d'Oulx, Pila, Cervinia, La Thuile, and Monterosa.
Milan airports: Not bad for Pila, Cervinia, La Thuile, and Monterosa.
Innsbruck: No airport is better placed. In 20 minutes, you can be in the village of Igls, where the men's downhill of the 1976 Winter Olympics was held. There is huge number of other resorts to look at, including Mayrhofen, Solden, Obergurgl, St Anton, Ischgl, Kitzbühel and Alpbach.
Salzburg: Again, handy for a huge range of resorts, including Schladming, Obertauern, Saalbach, St Johann in Tirol and Kitzbühel.
Zurich: Handy for Laax, Klosters and Arosa.
Verona: Provides best access for the resorts of the Italian Dolomites, such as Selva/Val Gardena.