Being a Canadian, going to Calgary, Banff, and Jasper has already been on my bucket list of things to do. However, finding the right time to go has always been tricky. The summer time in these areas is very short, about two months (July and August). If you go during that time, you have to not only pay a premium on accomodation and air fare, you also will be fighting with other tourists.
Luckily, one of the families we know through the homeschooling community was planning to go too and we decided to tag along and discover Alberta together. We were told that we should book our accomodation and flights early because prices went higher as the season approached. I would recommend you book your accomodation roughly 6 to 8 months in advance if you want a reasonable price.
We flew to Calgary on the 5th of June and it was noticably chilly still. We had our full winter gear so it wasn't a huge deal. If you are planning to go in early June or late early September, expect to encounter some snows.