I was just in Chamonix like a month ago...awesome place.
TONS of off piste terrain, crazy huge mountains, Mont Blonc right there, good party scene, lots of chill people, all around good vibe. Prices weren't terrible either, Definitely recommend that place if you're planning on skiing in France.
Theres a hostel called the Chalet Ski Station up this hill near the center of town. Super cheap place, like 16 euros a night. Right next to a bar and a gondola. Its run by a low-key old french lady (Margaret?) who pretty much lets you do what you want. Definitely recommend it. Also, this dude I met when I stayed there had a free bed for the whole season just for helping clean the kitchen once in a while.