You will struggle to find a hotel for forty dollars a night in vancouver ... even a hostel (shared dorm room) is forty dollars a night (a bit cheaper in the winter) ... "Shared Dorm Jun 1 To Sep 30 $36.00 $39.60 Oct 1 To Oct 31 $32.00 $35.20 Nov 1 To Mar 31 $30.00 $33.00" http://www.hihostels.ca/westerncanada/16... you could post on craigslist looking for a place to share for the time you plan to stay in vancouver ... http://patriciahotel.ca/rooms-rates - this hotel is thirty nine dollars a night in the WINTER and it is in a bad part of town, the website is way nicer than the reality ...
I work at a lower mainland hotel so am aware there are hotels/motels that charge nightly, weekly and monthly rates, and that owners/managers can set their own rate eg belog a posted given advertised rate, and yes we have guests that stay indefinately sometimes for months or years... so concur such an arrangement could be found in the Vancouver area. Here's where you encounter problems though, from my experience. The type of low-rent deal you describe very well might be found, the problem however is finding it - low-rent places don't put much money into advertising, don't have website and yellow pages with their name posted.
Best way to find them is either by others with personal knowledge or doing an internet search on 'vancouver motels' and using the 'contact us' feature asking. As for me, to get a place as low as $40 a night is given the Vancouver economy relative to hotel rates scraping the bottom. Things are generally more expensive in Canada than in the USA eg in Colorado where you were as Canadians tend to earn more in wages and goods sold than their Canadian counterparts - so $40 up here isn't relative to the $40 down there.
A $40 place could be found, but we're talking skid row... in range of $60 is more realistic. You'd have to alter your expectations a little, and try places like: 2400 Motel http://www.2400motel.com/ The Dufferin Hotel http://hotels.uptake.com/british_columbi... Go further east and try places like Maple Ridge Motel and RV Park http://www.mapleridge-pittmeadows.com/me...
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