If you're serious about mixing hiking with golf, you will be hard pressed to find a better area than Banff.
The ultimate combo would be Jasper/Banff. Jasper Park Lodge is the #2 course in Canada and Banff Springs is #9. Both courses have iconic hotels adjacent to the courses. Not only will you get some of the best golf and hiking, the drive from Jasper to Banff is along the Icefield Parkway, which is one of the world's most scenic drives.
Jasper is a bit out of the way for the less adventurous but if you are seriously thinking of Banff, then I'd recommend you do a Banff/Canmore trip. It's almost as good as Banff/Jasper with less travel and a more modest cost (stay in Canmore to save a few bucks). Canmore has a couple of excellent courses, but I'd recommend Stewart Creek (#28 in Canada).
We spend about 6 weeks a year in and around Banff and I'm pretty sure if there is a heaven it's a cheap imitation of Banff.