Montreal is not that kind to scooter and motorcycle riders. There are a few (and I mean very few) designated areas where motorcycles and scooters can park free of charge.
There is also a theory (which may have force of law, but who has the patience to find out?) that motorcycles and scooters can also park at the beginning, and at the end, of street parking slots designated for cars.
Here is an example of a motorcycle testing that theory just outside my office. The reflections from the sun made taking this picture difficult.

Notice I circled in white the "L" shaped marker designating where the permitted car parking space ends. Any car parking in the space that the motorcycle is in would surely be ticketed. The motorcycle? Maybe not.
In other two-wheeled respects, the City of Montreal is among a handful of progressive cities worldwide that make available a municipal bike-sharing program. The city is now covered with
BIXI stands..
Interestingly, just about every BIXI stand just happens to leave enough space at either end for a scooter to tuck in safely. This is a phenomenon that is sprouting serendipitously all over the city, and here is a great example, also right outside my window.

Close to 300 BIXI stands strategically placed throughout the city means that, in addition to all the existing nooks and crannies where I can park my Vespa, there are close to 600 more cozy spots just waiting for me.
So when it comes to parking for the scooter commuter, although on paper Montreal isn't as enlightened as Toronto, or as forward thinking as Boston, there is no shortage of great spots where you can park a Vespa.
For those of you living in Washington D.C., and for students and faculty at Washington State University in the Northwest, good news,
BIXIs are coming your way as well. More scooter parking for DC scooter commuters and Washington State students.