In reply to 2558benjamin:
It isn't much of a glacier any more, but the Glacier de Tre Les Eaux under the north face of Mont Buet is easy enough to get to, and there's a nice lump called the Gros Nol overlooking it that has excellent views for an overnight stop. An itinerary can be planned taking in Mont Buet summit, either of the Emosson Lakes, any number of the nearby summits (Cheval Blanc, Mont Oreb, Loriaz...), and of course the dinosaur footprints. Interestingly enough, if you access the Gros Nol from the Arete des Cristaux on the south face of Mont Buet, via the Tours de Buet, you can find a small section of the same fossilised beach that features the dinosaur footprints, a few kilometres away. This route is slightly off-road, and a sense of humour is recommended. The whole area is fairly off the beaten track, and a lot quieter than most other areas around Chamonix.
Another quiet option for bivvying next to a glacier with an interesting approach is along the Becs Rouges ridgeline, up above Old Argentiere. Slightly scrambly at times, but never challenging, the higher you go along the ridge the better the view gets of the Argentiere Glacier north faces (Courtes, Droites, etc), and you have the Glacier du Tour just next to you for harvesting water, making snow angels, sledging (carefully) etc. Watching the sunrise growing on the Argie north faces is, of course, spectacular.
You can do this route as a there-and-back, or turn it into a circuit by going up the dry and crumbly couloir under the Col du Passon, if you don't mind the inevitable peril that exposes you to. You can get there by crossing the Argentiere Glacier from Lognan, as one would in winter, or via a beautiful and deserted path cutting across the middle of the south face of the Becs Rouges.