Fly into Calgary and drive to Banff. Easy.
Not sure what you'll face weather wise there in October. I've been in summer and we had days of 70s and then a front came through with a dusting a snow at elevation. The winters are pretty tough there, but the plus is that the ski season is very long - we just skiied there in late April and it was fantastic. Their ski season is 178 days and is often perfectly skiable into May.
The Banff Springs Hotel is one a kind, and worth a visit/drink. The rooms are pricey and small, from what I hear. Banff is pretty, but it's a ski town so there's 'stuff'. If you want to get away from it, best keep driving.
Lake Louise gets all the praise, and rightfully so as it's beautiful. The Fairmont has a great location, but with its stucco facade feels more modern than the Banff Springs. Expensive, but good food (particularly the Walliser Stube). Just down the road, Deer Lodge is a rung or two below but maybe has more rustic charm.
I've stayed at the Emerald Lake Lodge, and the location is tops as it's harder to get to - they limit the number of cars that can drive up that way.
The hiking around and above either Lake Louise or Emerald Lake is just incredible. Highly recommended to hike to one of the backcountry 'Tea Huts' for lunch or a mid-day break. The entire area is an outdoor playground, and there are so many beautiful places to hike to - Bow Lake, Plain of Six Glaciers are two which stand out for me. The Kootenay Park has more geothermal activity which is an interesting visit. The Columbia Ice fields are also worth a visit, and even continuing up all the way to Jasper brings you to a different terrain and town vibe.
The Grizzly activity is no joke. You will see one. Know how to handle yourself in the backcountry and you'll be fine. Frankly, the moose and elk are probably more dangerous, but...