Flying to Spokane, Washington, if you can afford 2 or 3 more days and enjoy driving and seeing 2 or 3 more parks. Here is what we did few years ago.
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Day 1: fly to Spokane, drive to Glacier National Park, overnight there.
Day 2: Glacier NP, drive to neighouring Waterton Lakes National Park in Canada, overnight there.
Day 3: Waterton Lakes NP, drive to Banff.
2nd Last Day: Drive from Jasper to Sandpoint, Idaho. It is a long drive but half of it is in scenic Jasper/Banff/Kootenay National Park. A stop and plunge in Radium Hot Spring really refresh us and prepare us for the 2nd leg of the day.
Last Day: Easy drive to Spokane, fly home.
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A cheap lodging alternative in Canadian Rockies is to use family room in hostels. We stayed at hostels in Waterton Lakes, Banff and Lake Louise. You can cook your own meal in hostel kitchen. Canmore (next to Banff) offers cheaper lodging too. Jasper has a lot of "home accommodation" which is a unit in someone's house available for tourist to rent.
http://www.hihostels.ca/westerncanada/332/HI-Banff_Alpine_Centre.hostel
http://www.hihostels.ca/westerncanada/359/HI-Lake_Louise_Alpine_Centre.hostel