There are many good restaurants in the Banff Springs Hotel but expect to pay a hefty price.
We had a great meal at the Buffalo Mountain Lodge. Emphasis is on Rocky Mountain cuisine. had the Caribou which was delightful.
There is also a great sushi place whose name I forget. It's off a side road from the main drag and the sushi is prepared and put on a little train that circles around. Atmosphere pretty basic but excellent sushi.
Stay away from Le Beaujolais, the restaurant most often recommended. We found it pretentious, expensive and the cook had a heavy hand with the salt.
Good scenery and good chow do not often coincide, alas.
I was there ten years ago (studying at the Banff Arts Center) and had nary a decent bite for the entire two months. Calgary is The Big Town, but it's also pretty pitiful, food-wise (unless it's gotten a LOT better).
Are you staying at the Banff Springs Hotel? It is amazing, and if you economize and miss it, you'll kick yourself every time you see it (and it's biiig, so you WILL be seeing it).