I was in Montreal 3 weeks ago. There is a 3-day pass for bus/metro for $15 dollars if I remember correctly, I really recommend you buy it if you intend to explore all the classic touristic sights. Just google top things things to do in Montreal and you will have a pretty good idea what to do there.
I highly recommend checking out the Botanic Garden, the Chinese Garden they have in there is just unbelievable. The Mont Royal park is also nice, if you go there you should go to the view sight where you get a nice look at the city from the top. As for museums and stuff, there is the Biodome which I liked and the Museum of Civilizations.
I also recommend you check out Vieux Montreal (Old Montreal) at night, it has this european charm coupled with restaurants that I liked.
By the way, Montreal easily has the biggest amount of beautiful women in this planet.