My recommendations of things to do (these are my favorites, in no particular order):

If the weather is nice (above freezing), outdoor activities:

1. Vieux port
2. Place Jacques Cartier
3. Ile Sainte Helene
4. Parc du Mont Royal
5. Rue Ste Catherine in front of Place des Arts
6. Plateau Mont Royal, centered on the corner of St Laurent and Mont Royal
7. McGill University Campus

Indoor activities:

1. Eglise Notre Dame (the nicest church in North America, in my opinion)
2. Musee des Beaux Arts
3. A performance by the Orchestre Symphonique de Montreal
4. Oratoire St. Joseph (Montreal's Montmartre)
5. Biodome

A short drive on A-15 Nord:

1. Mont Tremblant ski resort (a mini-Whistler, highly recommended)

I would also add that in my opinion Montreal is the safest large city in North America. Though there is some minimal violence, it's almost always targeted (gangs, organized crime and domestic disputes). Random violence is almost unheard of. I cannot think of a single area of the city where I would feel unsafe. This includes St Catherine between St Laurent and Beaudry. Enjoy your stay!