I also live here, and I hate to say it, but I would focus your time on the Banff area, and not Calgary
April is a wonderful time to go. It won't be too busy, and it won't be too cold. I am not sure what your budget is, however if it allows, the Fairmont Banff Springs and Chateau Lake Louise are wonderful properties. As is the Post Hotel in Lake Louise. The spa at Banff Springs is an absolutely wonderful way to spend a day. I think you should be able to still skate and walk on the ice on Lake Louise in April?