Honestly I prefer going to the Pomeroy Mountain Village in Kananaskis, and visiting the Knordic Spa. Just took my missus there for her 40th!
But if you insist on Banff, check out the Banff Sushi House (cute little place with sushi served on a model train). My fave spot to chill and soak up the views is at the outdoor hot tub in the spa at the Fairmont - they allow the public to use the pools Mon - Thurs with a drop in fee. I think it’s $80 per person but you can stay all day if you want and it’s never busy like the Sulphur Mountain hot springs are.
The Bison is a nice dinner place, Waldhaus pub is cute and cozy. Second the moose and its cool outdoor pool on the roof.
But it sounds like you guys would REALLY love checking out the Banff Centre for Performing Arts. Great campus with lots of options for rooms and quiet places to chill out and soak up the nature, read, etc. They have an interesting library and other exhibits you can check out and the architecture is amazing. It’s a little out of the way from the main town so it’s also kind of a hidden gem but that baffles me.
Banff Centre
The On-It bus is the cheapest way to to from Calgary to Banff. I think it’s like $10/person but it only runs on weekends and is not as nice as other shuttles that go anytime you want. It’s about a 90-120 minute drive depending on conditions.