Intermediates should board the 16-person Bochard Gondola (Télécabine) and ski the groomed Bochard piste back to Lognan midstation. Or try the Chamois Piste next to the Combe de la Pendant to the triple chair.
If it hasn't snowed recently, the Pylones Run on the face below the upper tram softens around 11 am. On a good day it is possible to ski the Pas De Chèvre (Goat Path) down to the Mer de Glace and back to Chamonix. It is strongly advised, however, that you consult the ski patrol or a hire a guide to show you the route.
Three miles above Argentière, Le Tour appeals to low to advanced intermediates. Along with miles of rolling terrain that are groomed nightly, Le Tour offers spectacular views of the Mont Blanc. A number of lifts parallel the Swiss border. It's possible to ski into Switzerland, but you should remember your passport in case you miss the last lift and have to take a taxi back to France.
Also try La Flégère, which sits in the village of La Praz, roughly halfway between Chamonix and Argentière. Depending on the storm track, which can bury this resort under more than three feet of fresh powder, it's something of a secret spot. While crowds pound Les Grands Montets, La Flégère's long, rolling runs and short steeps often remain untouched.
And don't forget the Vallée Blanche. If you've never skied a glacier before and are an expert skier, it is not to be missed. Don't forget to hire a guide. In addition to keeping you safe, it's likely he or she will also be able to provide wonderful insights into the mountains and their history.