[Laceoflight]

1. Things we should definitely do :
My Montreal friends here have already done a wonderful work here :-)
I will only add my personal incontourbables to all of these great lists. In short I'd say :

• Free walk through le Vieux-Montréal.
• Walking Sainte-Catherine St. from Atwater to the Gay Village
• Climbing the mont Royal from Georges-Étienne Cartier monument near Parc Avenue to Beaver lake, and then up towards Kondiaronk Lookout.
• Heading to the Botanical garden, the world's second largest. Very impressive Japanese, Chinese and First Nations gardens. Impressive greenhouses. Maybe you could book a spot at the Tea ceremony ritual.
• Lachine canal by bike or canoe. You can easily rent. Be sure to stop by Atwater Market on your way.
• McGill campus is pretty cool when the weather is good!
• Exploring the Plateau
• Enjoying the sunshine with a blanket and some wine in the parks (Jarry, LaFontaine, Laurier...)
• Enjoying a meal and a beer on a patio (terrasse in French) on any great commercial street!
• The Chinese neighbourhood is mostly one street : De La Gauchetière. But it's kind of cool (though very small) anyway.
• Musée d'art contemporain and Musée des Beaux-Arts (Contemporary Art / Fine Arts). Centre Canadien d'Architecture (Canadian centre for Architecture).
• Saint-Laurent boulevard from Sherbrooke st. all the way to Bernard St., for shopping, eating, drinking, walking.
• Petite Italie is also a cool place. It's not as italian as it used to be though.

2. Things to skip :

• Olympic Stadium, definitely... The immediate surroundings suck and there's not much to do. You may wanna hit the nearby Insectarium or Planetarium or Biodome instead, which all offer a much more interesting experience.
• Never eat a poutine at La Banquise. It's the festival of salt and honestly, local montrealers usually don't go there. We prefer to eat it at small places that are not banners (Claudette or Patati Patata, for example)
• Crescent St. It's packed with tourists, essentially from anglo countries, it's kind of overrated, and honestly, bustling with douchebags. Not a bad place, but maybe you would prefer to hit Saint-Denis st. between Maisonneuve boul. and Sherbrooke St. (the Latin quarter), which offers a greater vibe, better places to eat or drink, etc.

3. Underrated attractions and things locals like to do
As a 30-year-old Montrealer, I'd say my favourite spots to go are located around these metro stations : Laurier / Rosemont / Beaubien / Jean-Talon / Jarry on the Orange line ; De L'Église / Charlevoix / Berri-UQÀM / Beaudry / Papineau / Joliette on the Green Line ; De Castelnau / Parc on the Blue Line.

• If you want to enjoy a great cheap night of good jazz/world/experimental music, be sure to hit La Casa del Popolo. One of the greatest places in Montréal in my opinion. Just on the other side of the street, there is La Sala Rossa, which is basically a theatre, but where you will find exquisite spanish tapas in an incredible ambiance (there are often flamenco dancers, etc.) In fact, Saint-Laurent boulevard is kind of cool in this area ; it's the Portugese / Latino neighbourhood of Montreal. Lots of great portugese chicken places and a specific vibe.
• One of the most underrated attractions is probably the Réseau des Grands parcs (Great Parks Network), which is constituted of many huge natural parks in many corners of the city. I especially love taking a walk at Parc de l'Île-de-la-Visitation, with its old mill ruins, its island in the middle of the river... I also enjoy Bois-de-Liesse park, in the north of the city ; the Islands as MartinMtl wrote ; Maisonneuve or Angrignon parks ; Cap-Saint-Jacques park (though public transit is long and sucks to get there)...
• Mont-Royal park is obviously a must-see, but I'd say that walking into the adjacent Notre-Dame-des-Neiges cemetary is quite an experience. It's the largest necropolis in North America. It's got a kind of Père-Lachaise vibe, especially in the upper part!
• If you have a chance to rent a car for one day, I suggest you to drive the Lakeshore boulevard from the old part of Lachine, then through Dorval, Pointe-Claire, Sainte-Anne-de-Bellevue, Senneville, Sainte-Geneviève... all the way to Ahuntsic. It's a great drive. Many great busy small village nodes (Lachine / Pointe-Claire / Sainte-Anne-de-Bellevue). Very surprising on a 2M inhabitants island! The lakes (Saint-Louis, des Deux-Montagnes) are beautiful.
• Montreal is kind of a craft beer Mecca. If you love beer, be sure to at least go to one of the numerous micro-breweries or brew-pubs scattered all around town : Dieu du Ciel! ; Isle de Garde ; Benelux ; Ma Brasserie ; BroueHaha ; L'amère à boire ; Etoh ; Harricana ; Vices & Versa ; Réservoir ; Le Saint-Bock ; Le Cheval Blanc ; Les Soeurs Grises ; HELM ; Station Ho.St. ; etc.

Special section : Le Plateau / Mile End

• Le Plateau is definitly a great place to hang out. Mont-Royal avenue is the traditional commercial street to explore. However, I'd say that if you feel like it, you could have a picnic at Laurier park (there's a supermarket right next to it ; if you want to have wine with your picnic, be sure to have plastic cups as glass is not allowed and to drink it before 10PM) and then head to some of the numerous cafés on Laurier avenue Est.
• You could do the same thing (picnic, wine) at parc LaFontaine also, near the pond. Great place to hang out if it's sunny. Guitar / weed vapes ;-) / people go crazy / it gets packed.
• In the Mile End, you should definitely walk Park Avenue north from Laurier to Bernard. And do not forget St-Zotique St. Mostly to feel the vibe, grab a bite, have a real nice coffee... There's De Gaspé street where you can find a bunch of independant cafés in an industrial setting. The nearby Champ des possibles is an urban wasteland that has been reappropriated by the citizens. If you are lucky, there may be activities such as urban flora identification, etc. ;-)

Other local commercial streets

• Wellington St. is the main one in the neighbourhood of Verdun. Cafés, new bars, good food. Popular vibe.
• Ontario promenade is the main street in Hochelaga. VERY popular vibe, mixed with young / kind of bobo establishments. Great street : local taverns, brocantes, nice bars (Monsieur Smith, Le Trèfle, Le Blind Pig, L'Espace Public, etc.), great restaurants, Maisonneuve Market. Good place for a night.
• Masson St. is the heart of Rosemont. Young crowd, essentially francophone. Lots of new restaurants with interesting concepts (Quai no.4, for example) and bars with young professionals. Popular and trendy.
• De Castelnau St. / Villeray St. / Jarry St. / Jean-Talon St. are the main and the most interesting streets in the neighbourhood of Villeray. Very close to Jean-Talon market. Small independant cafés (Larue & Fils, Chez Vito, Le Berri, Oui mais Non, etc.), great spots for a good simple meal (Le cochon caché, L'enchanteur, Tapeo, Le Petit Alep, Kitchen Gallerie...), nice local bars and/or micro-breweries (Le Pourvoyeur, Etoh, Huis Clos...)
• Beaubien St. / Saint-Zotique St. east of Saint-Denis St. are also popular places amongst Montréal's young adults.

The list could go on and on...
Ephemeral public spaces in the summer
Lots of interesting tactical urbanism experiments, great places to be :

• Le Village Au-Pied-du-Courant, an urban village created by yound designers every summer just under the Jacques-Cartier bridge, on an abandoned piece of land. Very festive!
• Shamrock place, next to Jean-Talon market.
• Castelnau place, over Sainte-Cécile church's parvis.
• Parc Stanley St. place, in Ahuntsic, next to des Prairies river.
• Sainte-Catherine St. in the Village, with the pink balls. It's probably in the guides though.

I hope you will enjoy your short stay