Hey, a response a month after you asked the question, but I'm starting grad school at McGill in the fall. If you want to live by yourself, I suggest finding a place west of campus (NDG, Westmount, Atwater) because it's way easier to find a one bedroom for less than 700. Westmount and NDG are more residential and you can find some real gems of apartments for cheap. Atwater is very downtown, lots of business, and big apartment buildings.
If you don't mind having roommates you can live wherever you want! If you're more concerned with being very, very close to school than there is a lot of housing near campus, though it relatively more expensive than other parts of the city for the quality you'll be getting. Plus you are guaranteed to have to endure drunk parades of undergrads at 2am on thursdays, fridays, saturdays, or whenever they feel like celebrating.
A lot of grad students live in the Plateau and Mile End. They're within walking distance of campus (usually 20-30 min walk max) and close to lots of of trendy bars, shops, cafes, and music venues. You can easily find a room for around 400-500 with everything included. If you're sharing, there's absolutely no reason to pay more than 550 for everything. One bedrooms in the area would probably be in the 600-800 range. I suggest living within walking distance to Parc Ave because the Route 80 bus that runs along Parc Ave comes so often, so it's easy to catch and you can get to school really fast (Parc ave is about 5 blocks from university avenue where mcgill is located; it's pretty much the most adored bus route for mcgill students).
If you want to stay in semi anglo areas then NDG, westmount, atwater, and mile end are english, for the most part. The plateau has a lot of students so it's pretty good unless you go too far east and then it's predominately francophone. A good way to pick up french, though! It's a good bet to stay west of st. laurent or within walking distance of Parc Avenue, Sherbrooke, or Pins Avenue so you can catch one of those buses to school. Being close to a metro isn't bad either, but I've found that it's not as convenient as when you're close to a bus route (the metro shuts down around 1:00am so you want to have other transit options if you go out late).
If you have any other questions about McGill, housing, entertainment, etc, I'll try to answer.