The best birthday surprise in the world is always an ice cream cake from Lic's. The bad thing about ordering one is that it always takes me a good half hour to remember that while the sign outside may say Lic's, it is actually called Leavitt's Ice Cream Shop (LIC's).
This is no doubt the best place in Calgary to get true Ice Cream. They have a ton of different flavors, and while it can be disappointing when my favourites get phased out, they always have something excellent to replace it. The ice cream cakes are "choose your flavours" if you call more than 24 hours in advance, so I have tried many combinations. Each one has been excellent, and the helpful staff will advise you away from the nastier combos.
I think that Lic's is perfect for both kids and kids at heart. I try to ride my bike down at least once a summer solely for the payoff at the the end. The store is conveniently located in Parkdale, just off of Memorial Drive and the bike paths, so by car or by bike, Lic's is where it's at.