Try Canmore. It's pretty far from Louise but is driveable and there are a crap load of rental places there (check vrbo.com) or just craigslist.
Also, a quick google pulled up two hostels in Lake Louise itself:
The Alpine HI
http://www.hihostels.ca/PM/en/lakelo...?sortcode=2.22
and
http://www.hihostels.ca/PM/en/abhost...?sortcode=2.19
and in Canmore:
http://www.hihostels.ca/PM/en/abhost...?sortcode=2.18
I just drove through there last week and was yearning to see snow. The skiing is incredible. Have fun.