Calgary West Camping
This campground is very close to the WeSTOC hotel. It is about 2km (1.2mi) away if you were a bird, but about 6km (4mi) if you drive because there is a major highway interchange between the campground and the hotel. It is probably possible to walk it in 20-30 minutes, but there may be stuff (like fences and ditches) in the way. This used to be a KOA many years ago. It has tenting sites available. It is on a hillside beside a major highway intersection and inside the city so it will not exactly be wilderness camping, but it is the closest to the WesSTOC hotel and the most convenient.
Calaway Park Campground
This is a campground associated with an amusement park. It is about 10km (6mi) directly west of the hotel. It is only a couple of minutes further away from the WeSTOC hotel since it is a simple fast run down the highway, so it is probably still a convenient option. There are tenting sites, and being a little bit out of the city it will be quieter (once the park shuts down for the evening) and is a bit cheaper.
Banff National Park