Whilst Verbier is the main resort, there are a number of smaller villages where you can stay and still access the 4 Vallées ski area. Le Chable is the village that lies directly below Verbier and is where the train from other parts of Switzerland (including Geneva) will bring you. You can access the Bruson ski area and the main Verbier ski area from Le Chable. La Tzoumaz is a small, quieter resort on the other side of the Savolyres from Verbier, and has gondola access to the main ski area.
Nendaz and Veysonnaz are further to the northeast from Verbier and are accessed from the road to Sion. Both villages have developed since they were connected to the 4 Vallées ski area and offer better-priced accommodation than Verbier. Nendaz has better access to the rest of the ski area, whilst Veysonnaz gives you access to the quieter slopes of the Thyon & La Printse ski area. You can see how the villages are connected on this map.