To be frank - there is more to life than golf.
But to give you
Golf options first (in the order of my preference:
Calgary G&CC (1.5 hrs. from Banff)
Blackhawk (Edmonton - 4 hrs. from Jasper)
Greywolf GC - Invermere (3hrs. from Banff)
Wolf Creek (1.5 hrs. north of Calgary)
Stewart Creek (15 minutes from Banff)
Options that I would choose instead:
We happen to be hikers and have made multiple trips to both National Parks
I've only brought my clubs twice.
BanffSightseeing at Lake Louise (stunning glacial lake) is popular
but I would recommend you hike
"The Plain of the Six Glaciers" - one of the more spectacular single day hikes - it's a must
Morraine Lake is the most beautiful place in CanadaIf your really adventurous they re-opened the "Via Ferrata" routes above Banff! - half day or full day routes are available for those not afraid of heights ...
Johnston Canyon is really cool - higher up is even better but a long hike
YohoI'm personally fond of the hike to
Yoho Falls in the adjacent (15-20 minutes West) - quiet - pack a lunch
Emerald Lake Lodge is also recommended for a place to stay
Go see Takakkaw Falls - our highest waterfall and pretty cool
JasperMorraine Canyon is a must - cool "narrow" canyon
Maligne Lake is great to get away from people
The Gondola or even low key Rafting on Athabaska is low stress
Also go to:Kootney National Park (nearby Banff and beautiful)
I happen to like the adjacent Columbia Valley a lot
Kicking Horse River has world class white water rafting
Awesome area of the world - almost moved there