Hi Chris. The Family Day long weekend is one the busiest weekend of our winter season. As such, it's popular and the budget accommodation gets booked up pretty quick. Rates fluctuate over the winter season and this is a peak winter as far as pricing. That being said - you're going to want to do a little homework to see if any of these properties have any availability for you at a price that is within your budget.
Here's a few suggestions of some great budget accommodation in Banff:
A family room at the King Edward Hotel.
A family room at the Banff Y Mountain Lodge - it's a hostel, with a great kitchen and common room.
http://www.ymountainlodge.com/
A family room or cabin at the Banff Alpine Centre with Hostelling International.
1-866-762-4122
hihostels.ca/westerncanada/…banffhostel.aspx
A family room at Bighorn Bed and Breakfast.
http://www.bighornbb.com/
A family room at the Elkhorn Lodge.
http://elkhornbanff.ca/
The Driftwood Inn, the Arrow Motel or Rundle Manor.
Caribou Properties: 1-800-563-8764
Check availability and rates at the Banff Lake Louise Tourism website.
www.banfflakelouise.com
Here in winter, if you're not doing any winter activities - you're going to be relaxing (enjoying town, having coffee shopping, relaxing at the Banff Upper hot springs) OR you're going to be sightseeing. In winter, the Banff Gondola is open: http://www.explorerockies.com/banff-webcam/ - $30 per person. As well, another amazing sightseeing alternative is going to the Teahouse at Mount Norquay. You can ride the chairlift up the mountain to the top! It's a bargain at $15 per person.
It's also possible to enjoy sightseeing with the help of your car. Vermillion Lakes Road, the Hoodoos Viewpoint, the Bow Falls Viewpoint, Surprise Corner, Mount Norquay Viewpoint and the Lake Minnewanka Road are all places you could enjoy a half day sightseeing by car.
Lake Louise is always a nice scenic drive along the scenic Bow Valley Parkway. In Lake Louise, you can enjoy a sleigh ride and coffee and a treat at the Chateau.