A bike left outside overnight is plenty of time for a thief to go through a U lock and cable. There's a thriving stolen bike market in Vancouver region. Just scan CL. It's crazy. You can quite easily pick out career bike thieves selling their wares there.
Your best bet is to pay a few bucks more and find an accommodation that allows you to store your bike either in your room or a secured indoor (as in kept in a lobby office or something).