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To ski for a day, even in poor conditions is worthwhile. There are many ski areas nearby that can offer reliable snow as a backup.
Both Mulletizer and verbier61 are taking a valid point and teasing it to its extreme. The equivalent would be me saying that the driest and deepest snow in December/January is in Lappland.
La Grave and Chamonix - Sick terrain will re-define "Big Mountain" and "Steep" in your world. You think you've seen it.... you haven't.
HIRE A GUIDE - find out who the best are, go to the guide himself and talk about what you want to do - don't hire one through your hotel. The hotel guides will be tailored to the group package tourist (and suck accordingly). If you go into a guide service and explain that you want to get scared, they'll be incredibly happy to hook you up.
Chamonix doesn't have a "better town" it has a real town. The place is more busy in the summer than in the winter which really says something about how complete and functioning the place is. If your dad needs downtime he'll be happy roaming the streets for a couple days.
Honestly, it's a different game out there. Nobody tells you to slow down, nobody tells you where to go. You want to huck that cliff over a beginner's traverse..... try not to hurt yourself. If you do, prepare to pay dearly for your rescue (that's not free either so buy the insurance), but nobody will frown or scold you for doing something obviously dangerous.
There's nothing sanitized about the mountains there. Look and know before you go there. Don't blindly follow tracks without knowing where they end up, they might just go to another town.
There are a TON of other places to go in the alps, many of which have been mentioned here. Fact is though V, C, LG are three of the best and a season at each wouldn't be enough time to fully explore their terrain. Pick 2 places and really get to know them.
I spent 3 years working in London with basically 3 weekends a month in the alps... somewhere. I probably hit 15 different resorts in that time and found myself going back to the above 3 again and again.
I'm jealous - have a great time.