Most homeowners and renters insurance policies of parents or guardians will cover their college student's belongings if they live in a dorm room. (valuepenguin.com)
This is especially good for students in a dorm room situation. (rentersinsurance.net)
To be fair, I was staying in a dorm room, and not a budget hotel room, so I can not comment on the standard of the private rooms. (hostelbookers.com)