I want to live in Montréal for 5 months without a work visa. How might I manage this?

I'm thinking of living in Montréal for 4 to 5 months, and I need a bit of help. I think this would be enough time for me to become fluent in French.

I'm 19 years old, female, American, et je me débrouille assez bien en français, je dirais. I have several questions:

• What the hell will I do?! I will not be taking classing or working (as I won't have a work visa). How can I occupy my time in a meaningful way?
• Should I try for a visa? How difficult are they to obtain? It'd be nice to have some sort of income.
• Can you recommend some neighborhoods? What are their vibes, level of safety, price ranges, etc?
• How can I search for roommates?
• Are there other questions I should be asking?

Merci d'avance!