Go to Old Montreal. Although being European, it may not impress you as much as it impressed me.
Yeah, old is relative but it is still nice but touristy.
The botanical gardens is great, right by Stade Olympique which has the funicular up to the top (used to be the arm for the retractable roof) where you can see the view of the city. St. Joseph's Oratory is a nice building to tour, also has a nice view from the hill.
Dieu du Ciel for incredible creative microbrews that are finally available in the US but cost an arm and a leg here.
Get a smoked meat sandwich and poutine. Ask locals where the best are, not all smoked meat is created equal (ib4 twss).
See a lower level Junior game- I saw the AAA Valleyfield Braves once when I was up there. Something about the atmosphere in a small dirty arena in Canada....