Montreal - is an island with many small cities spreaded on it. With a while some of them grew up so much that joined to their neighbours and now driving through the city you will not notice when one is finished and another is started.
Most of sights, you want to see, located in downtown of Montreal, in french it is named "Ville-Marie" or "Centre Ville". Downtown of Montreal theoretically may be divided in two parts: Old Port (Vieux-Port - in french) and modern/business downtown - includes central part of Ste-Catherine street and its surrounding (be careful, in Montreal there is another street with similar name "chemin de la Cote Sainte Catherine").

Definitely it's worth of it to spend 2 hours for walk through Old Port. This is a historical centre of Montreal, it's source. A couple small avenues with stone buildings and ways coming to a quay. Now those building mostly used as touristic stores and restaurants. Personally I prefer "Les 3 Brasseur". Not very expensive, good beer, pork fore end, huge barrel with free peanuts - nice place for friendly drink.
Beside the center square there is a small historical museum. It shows the way of life a couple centuries ago, some ancient items, old paintings. Guide will tell you about first settlers, wars, how province Quebec is appeared and what means the history of Quebec for their habitant (it will not take more than 1 hour).
On summer time you can have a very nice walk along the quay. It is the place for many small street festivals and good place to watch the fireworks in period of firework festival (june-august). On winter time there is cleaned place for skating right on the river. Huge tent is installed over here with a bar inside, where you can take a brake with a couple drinks. On the quay itself usually installed some barrels with a fire for the heating, built labyrinth from the snow, so it can be still a nice walk even in a cold weather.
Here in the Old Port located a church Notre-Dame.

Modern downtown - is a business centre of Montreal, mostly consist of offices, because of that a lot of festivals goes here all nights through. It will take a lot of time to investigate it all over. Probably you can start just with a walk along the Ste-Catherine street somewhere from subway station Atwater or even from Guy-Concordia (few closer to the center). On a summer time you can find here some street artists, musicians, painters and clowns. Along the street located a lot of shopping centers, restaurants, tourists stores, cinemas, strip clubs, dancing schools and etc. Do not be shy to turn on a small pretty streets, for example street Crescent is a very popular place.
It is pretty difficult to find a parking place along the Ste-Catherine, but behind the buildings faced on it you can find a lot of small well organized and secured parking. Price is around 10-12 dollars for a half of the day. Pay attention on signs, many skyscrapers have underground parking.