There is some great camping in Kananaskis, just outside of Banff. You can use the camp ground as your home base and then set out for a multitude of day trips. There's great hiking and mountain biking. I spent many weekends here in my old VW Westfalia.
Welcome to Kananaskis Country
Jasper is further north and I've not been there for years. There is some great camping in the Provincial Parks, if I recall.
I'm more familiar with the Vancouver area now, so if you have any questions, feel free to ask.
Enjoy your trip!