How to configure cups to allow remote printing with authentication and local printing without?

Add the following lines to you snippet:

Allow from localhost
Allow from 127.0.0.1
Deny from all

and change the Order line to

Order deny,allow

so it reads:

<Location />
   # Restrict access to the server 'root' location...
   Allow from 192.168.1.0/24
   Allow from localhost
   Allow from 127.0.0.1
   Deny from all
   Require valid-user
   Satisfy any
   Order deny,allow
 </Location>

Should this not be sufficient, add the same settings for the <Location /printers> and the </Location /admin>:

<Location /printers>
   # Restrict access to the server's shared printers...
   Allow from 192.168.1.0/24
   Allow from localhost
   Allow from 127.0.0.1
   deny from all
   Require valid-user
   Satisfy any
   Order deny,allow
 </Location>