Where in my files can I find the stock browser's Favourites stored? Where on the storage of my phone can I find the stock browser's Favourites?  I want to backup that folder.

OS: 4.1.1
S3
All the data for the S3's stock browser are stored in /data/data/com.android.browser/, but just like any app's private data directory, you can only access that if your phone is rooted.

Rather than try to find app data to back up and manage that process yourself, I strongly recommend you to use one of the many existing backup apps out there, or to use adb backup.