What is the best time of year to visit?
What do you want to do there?
Let's start by narrowing down a season ... do you want a winter holiday (skiing, snowboarding, snowshoeing etc.) or a summer holiday (hiking, canoeing, horseback riding etc.)?
Are you willing to trade better weather for cheaper accommodations?
It's like the others have said it depends what you want to do. Winter has it's own beauty but if you are wanting to hike or see some of the higher alpine terrain (i.e. around lake moraine or lake louise) then july-mid-september is the prime time. The issue there is that it's the time everyone wants to go.
I would highly suggest not doing April-June. You can get cheaper accommodation in the spring, but as the winter snow pack is melting trails are muddy and passes, alpine terrain are inaccessible.
Go March and April. The mountains look more majestic and the popular sites are less crowded. You already know how to drive in the snow.