My two most memorable dining experiences in Banff have been at the Eden restaurant in the Rimrock Hotel and the Banffshire Club at the Banff Springs Hotel.
Eden is like River Cafe in Brooklyn, all the tables are either by the window or along the back wall with a good view out of the window to the mountain view. The menu is prix fixes only, usually among 3 choices. It is a tasting menu, i.e. many, small portions with wine recommendations. Food was delicious and when I thought one of the wine pairings was not working, the sommelier brought me a different glass of wine to try. My only complaint was the elevator type of music in the restaurant, which wasn't loud but not fitting to the style of the restaurant.
The Banffshire Club does not have a view but in addition to a prix fixes menu, it also offers a la carte choices. The wine list is extensive. The food was among the best I've had anywhere in the world.
Both places have very attentive service and both are expensive. In fact, the Banffshire Club is more expensive than any restaurant in Calgary, but then, most things in Banff are more expensive than in Calgary.