We would stay in the Albergo del Popolo in Rome back in the 1960's and 70's. It was run by the Salvation Army and it wasn't pretty or fancy or hip, but it was CHEAP and a safe place for young women to stay and had decent (and free) food. We stayed in a convent once but if you weren't in by 10 p.m., the gates were locked and you were on your own.