Onsite or Offsite backup storage

We do nightly backups and currently we take the previous days tape and put it in the bank. I want to get away from doing that I want to know if any of you guys have had experience with keeping backup data onsite. What kind of security issues do you have? These kinds of questions my CEO is going to ask me and I just want to know what I’m up against. Do you know what the flash point is for media devices?

Any help welcome.