Chez Parée should be your stop
Seriously, it's been years since I have been there.
Schwartz for smoked meat sandwiches.
Go for a stroll around Old Montréal, and Mount Royal.
As a sports fan I'm a sucker to see places like Olympic Stadium, but it'd be more to see how weird and odd that it's no where near downtown. But the Biodome there is cool.
I don't know if they still do the fireworks competition but they were always awesome (used to be different countries put on a display twice a week).
See what's going on, there's always a festival of some sort going on.
I love their subway. It has a smell I can't explain. It doesn't stink, but it's distinctive. Every station is different, and some are just gorgeous.
LaRonde and Expo 67 is cool.
Enjoy some of the pubs, bistros and the uniqueness of everything being French and how neat it is that literally everyone speaks English (in downtown Montreal, get outside of that and that changes).
It's nothing like Calgary (it's nothing like any city I've ever been to) explore and enjoy.