Hey Richard,
Here are my recommendations for MTL:
Of course check out what’s available on AirBNB but if you’re looking at hotels on a budget have a look at ITHQ hotel. It’s a government run hospitality teaching institute but you get an amazing stay for 180$. The rooms are nice, you get an awesome free breakfast (freakin’ smoked salmon) in a proper restaurant setting, free parking and its on top of a metro station right downtown.
The Musé d’art contemporain (MAC) usually has good expositions going on. The Belgo Building right accross the street also hosts a bunch of galleries/studios. It’s a much more grassroot operation but if you’re an art nerd have a look at their website for what’s going on.
I think its hard to appreciate Montreal without a minimum understanding of French Canadian history. So to get to bits relating to Montreal’s architecture and infrastructure, for the early part of the 1900’s, Quebec was quite behind the times in terms of education, infrastructure, general emancipation and a lot of the wealth was held by foreign or anglophone stakeholders. This was namely due to a very conservative government with deep religious (catholic) ties. That historic period is usually called Grande Noirceur (Great Darkness) which ended in 1959 with the death of premier Duplessis and lead to the Quiet Revolution of 1960-1970.
This Quiet Revolution was a very sudden change of very deep and fundamentals of society. Quickly going from the some of the lowest education figures to a full overhaul of the education system including its quite unique publicly funded pre‑university colleges and cheap public university network. Also notable are the nationalization of electricity production, massive secularization, investment in culture and ultimately the rise of a national identity and ultimately will for independence (for better or worse).
Getting back to how this relates to the city of Montreal. Montreal feels in a lot of ways like a time capsule to the 60’s and 70’s where the metropolitan area population almost double in 20 years and where massive investment in infrastructure happened. The Montréal Metro was built in that period and a lot of stations haven’t been remodeled. The World Exposition of 67 with Habitat 67, Fuller Dome which is now an environment museum, the France and Quebec pavilions which are now Montreal’s Casino. The city was also shaped a lot by the '76 Summer Olympics.
(Honestly, I wasn’t planning on writing an essay when I started…)
This one’s going to sound like a super touristy thing but Saute Mouton Boat Ride. Essentially, you hop on a super powerful jet boat, they take you from the Old Port to a set of rapids and basically jump around the rapids. It’s kind of like a jet-ski ride scaled up about 10 times. A lot more fun than I thought (you’ll end up completely soaked and slightly shaken) and you get to see the city from a nice vantage on your way to and back from the rapids - great for a first day to get oriented.
As others have mentioned have a look at what’s going on at Place des Arts and in terms of festivals through the city, there always seems to be something going on culturally in Montreal…
Have a look at the Société des Arts Technologiques (Society of Technological Arts) its really central and often has some neat shows/events. Video games and live entertainment tech (show lighting/projection design and immersive environments) are pretty big sectors in Montreal and the SAT is a hub for that in some ways.
Speaking of lighting, Jacques-Cartier bridge has been setup with a full lighting setup by Moment Factory which if I understand correctly is light up every night - I haven’t had a chance to see this yet.
Marché Jean-Talon is quite nice. There’s a bunch of vendors inside and out with a neat showing, the vibe is usually pretty fun. Could be a good spot for lunch if you’re in the area or if you want to grab some ingredients to enjoy at an AirBNB.
On your way back to Toronto, consider a hop in Ottawa. If you do, stop at Beau’s brewery in between Montreal and Ottawa. There’s a bunch of stuff going on in Ottawa right now with the 150th celebration of the confederation. If you’re a runner, you might enjoy a hike in Gatineau Park federal park which has some beautiful trails and will get you close the touristy/hippy but very nice villages of Chelsea and Wakefield.