The Chamonix Valley is a world famous winter sports destination - and deservedly so. The apartment in Argentiere is ideally located for access to a variety of ski areas, offering a variety of skiing and snowboarding terrain.
At just under 3300m and with a maximum vertical descent of aroud 2000m, the Grand Montets offers some real mountain skiing. And with the uplifts being just a short walk from the apartment, chances are you'll spend a fair bit of time here. However, whilst clearly appealing to the more experienced skier, there's a variety of runs around the Lognan and Plan Joran to suit beginners too.
At the foot of the lifts you'll find the Panda Club for children. In addition, there's the nursery slopes at Les Chosalets, ideal for the first time on skis.
Located at the head of the valley Le Tour is best accessed by the Chamonix free bus or by car. Although there are some harder runs, the terrain is more typically open cruising on blues and reds. Recent improvements to the link to Vallorcine have really improved the area.
La Vormaine is a small nursery area in Le Tour and is another great location for trying skis for the first time or perhaps taking the kids sledging.

These areas are located on the north side of the valley making them south facing with great views across to Mont Blanc. Again, both are best accessed by the Chamonix free bus or by car, though there is the possibility of using the train as well.
The areas do have a connecting lift though they are really two separate areas. La Flégère offers some great sunny skiing to a wide variety of abilities, whilst more advanced skiers and boarders will find some of the terrain at Le Brévent a real challenge.

Located on the far side of Chamonix, this is a good place to head when the higher mountain areas are storm bound. Tree skiing is a real delight and the area is good for both beginners and intermediates. Its slightly less popular with boarders however, as there are a few drag lifts and some flatter areas between some of the tows.
There are of course, further options for those that want to go looking for them. For example, St. Gervais and Megève are within easy driving distance.
And there's also plenty of Off Piste adventure to be had, not least of which is the descent from the Aiguille Du Midi via the Mer de Glace. Its a day out to remember - but the advice is always be properly equipped and unless very experienced mountaineers its best to hire a guide.