May or June is too soon for Banff. It is beautiful in May or June (snow covered mountains), but all the famous lakes will be frozen and it might be snowing at that time. I was there at the end of june and it was still snowing and bit chilly. I enjoyed it a lot more at then end of July. You can go canueing and hiking and it is just absoultely stunning. Watch out for a grizzly. =)