thats a great park and is best viewed from back country trails. If I were you, I would rent all the gear you need and spend the entire time hiking from the the east central area up to the Canadian side. There is a shuttle you can take back down.
If you don't want to do an extended back pack trip, then consider a overnight trips where you go in a day or two, and then back out.
Ptarmigan Tunnel is something you should see whether you do it as a day hike or part of a larger trip.
You can also rent a bicycle and ride up and back down Going to the Sun road.
The lodges around the park are great and a good place to rest and recover.
Banff and lake louis are awesome too, but are very far...plan on driving at least 1 day each way.
Oh, and don't be surprised if it snows.