We live midway between Mont Royal and Parc Lafontaine, two of the green parts of the city.
Mont Royal is huge, which makes sense, since it gave its name to the city. There are paths for biking, running, walking, or skiing in winter. One can climb to the top and take in the view from the Chalet, directly over downtown Montreal, where the St. Lawrence valley stretches out below. From the Eastern side there’s an overlook with a view of the Plateau and the Olympic Stadium. Lower down, near du Parc and the Parc Jeanne Mance is the iconic Monument à Sir George-Étienne Cartier, where crowds gather to play drums (tam-tams) every Sunday. Good picnic areas either near /just up from the monument or behind the Chalet at the top.
The huge Mont Royal cemetery on the mountain is also worth a visit.
Parc Lafontaine is beautiful any time of year. Great for picnics in the summer, around the ponds. It’s always full any time it’s warm. In winter the trees are lit and the lower pond becomes a skating rink.