There is a platueu just East of the Aiguille du Midi, which has a cable car go up to it from the valley.
This is as high and as close as you can get to Mont Blanc without being a professional climber or whilst being escorted by someone who is. You're in the shadow of Mont Blanc here - probably 2 km's away from its last ascent.
You have to walk most of the plateu until you get to some better piste conditions towards the Italian border as you're walking across a crest which I believe is known as the 'Walk of Death'. This requires a guide of which can be organised once at the Aguille Du Midi. You can then ski back down into the valley having done the walk - although it's one of the more difficult black runs in the valley.
Alternatively, you can ski down Vallee Blanche and le Mare du Glace which also requires a guide.
(As already pointed out.)