In reply to Philo22:
You can have a good time in the mountains around Chamonix by yourself. I've done this several times for a week or more when my partner has had to take off early.
Depends on your experience and (for a few of these below) how happy you are with exposure. But these below are all away from wet glaciers and can all be done by foot from the village. Eg. if you ignore cable cars and trains the walk in from Chamonix to Ag Gouter summit is a great 2 day expedition (camp at Tete Rousse site) to almost 4000m.
Ag Crochues
Ag du Belvedere
Scrambles on ridge around Brevent
Ag Gouter (short bus to Les Houches)
Mer de glace walk (only on dry glacier)
Balcon walks both sides of valley scramble up whatever takes fancy
More techy scrambles (need backup ab rope):
Ag Moine (or at least Couvercle hut VF kit for ladders?)
Ag L’M (or at least the col before final scramble)
Ag Pelerins (depends on conditions very exposed)
From Italy (take bus through tunnel)
Petit Mont Blanc (3 days total from Chamonix)
Have fun.