Best place in Montreal for an outdoor lunch?
This is a personal preference thing. Old montreal on the greenspace along the waterfront would be my favourite, there are picnic tables, benches and you can walk, bike, skate or just watch the street artists, and performers near the water when you finish your lunch, or further up on jacques cartier square usually some free entertainment going on. I have even seen people string up a hammock from the trees near the archeology museum after their picnic! You could go further afield by taking one of the water taxis. With a young family though I might head to the mountain in area of Beaver Lake, I always found Parc Lafontaine too crowded during the summer period.
Westmount Park in the back part is pleasant but you can get a $450 ticket if you give a snack to the squirrels!
If downtown and you want an urban milieu you could head to the place des spectacles, they currently have the 21 balencoire exhibit til May 23 where you can make music by swinging and there are a lot of adults enjoying those swings. Not much green space but you could have a lunch in the square and enjoy a drink or cocktail on one of the resto- terraces. http://www.youtube.com/watch?v=jEH1-g...
If you did not mean picnic lunch, the inside patio at jardin nelson is attractive for lunch or brunch and also has music http://www.jardinnelson.com/en/home.html
Depending on what you're looking for (good food, good terrace, comfort, etc) I suggest trying any of the following on the next nice day we have. il Cortile, Joe Beef, El Messon, Le Saint Sulpice (the hotel, not the bar) and Santropol.
Parc nature de l'Ile de la visitation on north shore of montreal island has a resto terrace in a unique location stream-side beside the ruins of some old water-powered mills (old like 1726 – 1960). Bistro des Moulins on rue du pont (possibly dupont).
There are many fine parks along Montreal's shoreline on all parts of Montreal island if picnicking or eating takeout in scenic locations is your request.