Le Bettex (and Megeve)
The car park at the village of Le Bettex is a 5 minutes drive further up the mountain to 1400m altitude, and this usually has good snow.
There are nursery slopes, and two ski schools: ESF (Francais), and the International Ski School. There are also a number of shops, ski hire, bars and restaurants.
From Le Bettex, the gondola runs back down to St Gervais or further up the mountain to 1800m. Chair lifts can then take you to an altitude of 2300m. The local 'Domaine Evasion' ski pass allows you to ski this area - down into St Gervais, over the mountain to Megeve, and close to the peak of Mont Joly. There are plenty of easy and wide intermediate slopes, as well as some more challenging runs, many with views of Mont Blanc; and good fast lifts.
Non-skiers can hire snow shoes at Le Bettex, and ride the Gondola up the mountain for some great walking. There are also good cross-country tracks from Le Bettex.
Chamonix
If you are after really challenging skiing, or the snow conditions are variable, the 'Mont Blanc' regional ski pass, covers both the local area, and many others around, including Chamonix, Les Contamines and Les Houches, giving access to the most demanding slopes, and off-piste powder.