How do I access Notes backed up from iPhone onto Mac without using an iPhone?

I don't think you can. I believe backups can only really be used to restore a phone. Other items you transfer using syncing processes. I don't have an iPhone but my wife just went through all this at the Apple Store last week. She was told she had to sync notes she created on her iPhone to her computer through her iCloud account (if you have an AppleID you have one) unless they were in the "only on my iPhone" section in which case she would have to attach each one individually to an email and send them to herself. From reading the web about notes they are really mini e-mails, not a simple text document that can be moved from place to place.

Backups are stored in a format meant only for use when restoring. If the only copy you have is in a backup then you will need 3rd party software such as http://www.wideanglesoftware.com/ibackupextractor/

If the notes are still on the phone and you are looking for an ongoing way of accessing them, the following has sync instructions iOS: Syncing Notes