To the east of downtown Montreal, you'll find the Parc Jean-Drapeau spread over two islands in the St. Lawrence, St. Helen's and Ile Notre Dame. A significant space for both culture and entertainment, you'll probably spend your time here if you want to catch any of the major outdoor concerts that happen in Montreal or the most watched Formula One race in the world, the Montreal Grand Prix (the last weekend in February). For the sake of entertainment, there is a snowboarding park, a casino, an amusement park (La Ronde, a Six Flags establishment), a man-made beach, and a lot of green area in which you may find yourself mingling with locals for impromptu outdoor games.
On the cultural side, there is the Biosphere (an architecturally unique, spherical building that houses exhibits drawing attention to contemporary environmental issues), an outdoor art gallery, and the history on display at the Stewart Museum and the Fort de I'lle Sainte-Helene.
About 10 minutes outside downtown, this park is an excellent place to find yourself when you're on the lookout for something fun to do during the day that doesn't include ambling aimlessly through the city streets.