Chamonix is definitely geared towards the expert and advanced intermediate rider, and beginners may want to look elsewhere. There are six different ski areas located along the ten-mile long Chamonix valley, which include Le Brevent, Les Houches, Le Grant Montets, Le Tour, Le Pratz, and the Valle Blanche run. (See my journal entry on the Augille du Midi for more information on the Valle Blanche run.) If this isn't enough action for you, Verbier, Switzerland is within a two hour ride, and Courmayeur, Italy is just a short drive away through the Mount Blanc tunnel.
The best ski areas by far were Le Brevent and Les Grand Montets. Being less liability-conscious than their American counterparts, the resorts in Europe have a very liberal out-of-bounds policy. Translation: there is none. You are basically free to go wherever you feel is within your ability. My most amusing (and slightly harrowing) experience came at Le Brevent when I met up with a fellow American and decided to try out some of the chutes. We shared a chairlift ride where we were able to see a number of chutes on our way to the top. We picked one out which was fairly steep, but appeared to be wide enough to at least carve some decent turns. The terrain looked much different from the top, however, and we ended up entering the wrong one. The chute narrowed down to about three meters wide, and was extremely steep with rock outcroppings on both sides. After a little praying and alot of sideslipping, however, we made it to the bottom relatively unscathed.