Right in front of the Old Port of Montreal there is a park called Parc de la Cité-du-Havre. As close as this park may look to the old port, truth is that it is ride away, yet it is worth it, the 360 view of Montreal, the Jacques Cartier Bridge, and the Jean Drapeau Island; is priceless.
The bike ride or the wake to this island is worth it as it is a nice walk along the water, through the hidden bike paths of Montreal.
Here is where you can see this park on the map.
It is a 4.5 Km bike ride from the old port, and a almost a one hour walk.
Still definitely worth it.
Here is another beautiful island to visit in Montreal