When Syncing OneNote 2013 notebooks to SharePoint Server for the first time you do not have the option to save these to an on-premises SharePoint Site.
You will need to first save to "My Computer" and input the SharePoint server URL. After this you will have a new location titled "Other Web Locations".
When you open OneNote 2013 for the first time it will prompt you to connect to the cloud. You can close this with the X in the corner if you do not want to connect to the cloud.
Select your update Settings.
When trying to open a Notebook from SharePoint Server you do not have any options for an on-premise site. You only have SharePoint Online or OneDrive.
This also happens when you attempt to create a new Notebook. You need to select "Computer", Type a name for your new Notebook and click on "Create in a different folder".
Type in the URL of your SharePoint Site.
Browse to the Document Library where you would like to store your new OneNote Notebook, give your Notebook a name and click "Create".
You now have a new option called "Other Web Locations" when attempting to open or create new Notebooks.