The priority might change if skiing were not your #1 activity:

1. Whistler has a purpose-built base village, and is clearly the most convenient for a ski vacation -- a great ski resort experience. The ski area is huge and very well laid out.

2. Lake Louise is in a drop-dead location but it's a 5-10 minute drive from Downhill skiing, while you can cross-country ski right out the door. It is a smallish, pretty much self-contained hotel, probably because it is so isolated (there is one other resort -- the Post Hotel -- about 5 minutes away, with one excellent restaurant to lend some variety). The skiing is over a huge expanse of mountains, with a more haphazard layout than Whistler because it evolved over a longer time, but it's also a LOT sunnier than Whistler. As long as you're driving, you'll probably drive a bit further once or twice to Sunshine (above treeline skiing). Neither the mountain nor the hotel is in anything you might call a village.

3. Banff is the most interesting hotel (history, facilities) in the most interesting village of the 3, but it is by far the least convenient to skiing. There are 3 mountains in the area, and the all-around best is Lake Louise, which is the furthest away.

If you do pick Lake Louise, you might spend a night or two at Banff, and use that as your base for Sunshine / Norquay, the other mountains in the area.