We lived in Calgary late 2002 - late 2004, so we spent a good deal of time in the Canadian Rockies.
As far as resorts local to Banff are concerned, our home hill was Sunshine Village. The short chutes off of Goat's Eye are lots of fun (watch out for rock sharks when it's been windy--keeps you on your toes), and there's even in-bounds *extreme* terrain, which requires a transceiver and shovel for entrance. Also some good blacks off of Tee Pee Town (can be a bit rocky) and Angel Express chairs. The Continental Divide chair offers some astounding views of Mt. Assiniboine on the rare days when it is clear enough to see that far. . . but beware this chair when it is *Canada-cold* and windy. Whoo-wee is it ever unpleasant to sit in the unprotected teeth of the wind on this baby.
And if you're looking for something unusual, you can even stay TRULY on-mountain at the Sunshine Inn. Sunshine's *village* is actually on-hill, as you have to take a long gondola from the parking lot to get to the skiing. At night, if you stay at Sunshine Inn, it's you and the stars and a few other guests. Nothing fancy, but it's kind of a cool feeling. And very definitely first tracks in the morning.
Lake Louise is a great resort as well, big (something like 4000+ acres), with terrific views of the Lake and Plain of Six Glaciers. Biggest challenge for us was navigation, as our favorite areas were the Back Bowls (Chunky's, Ridge Run), Ptarmigan (Ptarmigan, Ptarmigan Chutes), and Paradise (Paradise Cornice, Gully 7). Navigation between these areas makes laps, er, difficult. Particularly if you want to do laps in the Back Bowls.
You have to take the world's longest, steepest, most painful platter to the top, drop in, ski a great run, ride a bunch of flat back to the Paradise Chair (painful for my husband the snowboarder), ride the Paradise Chair up, drop over the front side, and work your way back across the front of the mountain for another painful ride up the platter. Which is, of course, why the snow can be so spectacular in the back bowls. . . almost no one is making the effort required to do laps back there!
As for Norquay, well, it's small, but it's very convenient to Banff and a great way to warm up. . . and if you only want to ski for a short day and don't have a pass, then it's great because you can pay by the hour. And there are a few fun runs there, too. Nothing epic, but certainly not bad.
Banff itself is one of those funny ski towns that manages to be both touristy and charming at the same time. Lots of signs in Japanese for the tourist crowd, lots of T-shirt shops, and then some fun little gems like a good bookstore and an old-fashioned candy shop with things like horehound and swirly lollipops and all of the funky sweet things you used to see at grandma's house. The Banff Springs Hotel is worthy of its grand-dame status, even if a scattering of the sleeping rooms are a bit threadbare. The views from the Rundle Bar are spectacular, and the public rooms make a great wander. Also, it's worth saving your pennies to visit the spa for a treatment and get access to the pools. They have a European-style area for taking the waters, with pools of various temperatures and depths, and peaceful places to sit behind waterfalls and feel very relaxed and pampered.
If you're more likely to ski Louise than anywhere else, and have some coin, you could consider staying at Post Hotel (a much better choice than the very touristy Chateau Lake Louise, IMHO), which has a world-class restaurant and wine cellar (I know because my in-laws treated when they came to town
) and some lovely rooms. Once you're inside, you'd never guess how close you are to the Trans-Canada Highway. Or, stay at my personal favorite place in the area if you don't mind driving (and, again, opening your wallet). Ah, Emerald Lake Lodge, camp for grown-ups.