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Hostels (google them) are usually cheaper than hotels but you have to be wanting to be with other people.
Bed&Breakfast could is another suggestion (but usually not cheaper).
Try university lodging; they sometimes rent out student apartments in the summer (but at the time you will be here it will be probably be over).
For example, UniversitΓ© de Montreal: http://www.studioshotel.ca/
If really cheap, you could "couch surf" at someone's apartment (I don't approve it, so look for it yourself).