Chamonix is a mountain town in the south-east of France, famous for its proximity to Mont Blanc. The town has been named the Aspen of France, being a haven for skiers, snowboarders and hikers alike. Every summer and winter season it is loaded with celebrities and all-around cool people, making it hard to get reservations. It is possible to stay cheap though, if one books ahead of time - for $40 American one can get a nice double with a mountain view. Unlike anywhere else in France, the tourist center is actually useful and will track down deals on just about anything.
The two things I would consider a must-do are taking the lift to Aiguille du Midi, near the top of Mt. Blanc and hiking down (bring boots!) and walking down the long road facing Mt. Blanc until the little lake and forest are reached.
The food, btw, is great, the cheese and meat shop has some smoked items that are out of this world, and the candy store's chocolate covered cherries are like nowhere else.
Thanks to Biker for the correction! Aiguille du Midi is actually a kilometer below Mt. Blanc, at a mere 3842 meters.