I'm from Montreal. Here's a link for sightseeing in MTL that could help you: http://www.tripadvisor.com/Attractions-g155032-Activities-Montreal_Quebec.html
From the link, my choices would be:
-Mount Royal (Walk up there and enjoy the view of the city. Nice place to go to see greens right in the middle of the city.)
-Notre-Dame Basilica (Old church is old and really nice. Contrast with the buildings.)
-Old Montreal/Old Port/Old Quays (Just a must to walk around St-Jacques and to enjoy the old European feel of the surroundings. Lots of nice restaurants too.)
-St. Joseph's Oratory (If you are in the old Catholic buildings, this is a must. Big and old and pretty.)
And the other stuff depends on when you plan to visit MTL. There's quite a few festivities during summer. (24 of June, 1st of July, Jazz fest, F1 racing)
Late June and all July, each Saturday night is the International Fireworks festival, where pros from all around the world come and give us a really good show http://www.internationaldesfeuxloto-quebec.com/en/
For the city of Quebec, I'd say, check the 1st link for more info on Quebec, since the last time I've been there, things might have changed a bit regarding the festivals and such. But the Frontenac Castle is a most and walking around the old city is just amazing.
I hope it will help find some nice things to do. MTL is always buzzing during summer time, since we have snow the other 9 months or so....