If you just want to know your codice fiscale number go to www.paginebianche.it and enter your details. It is not a private thing like in North America, it is simply a combination of your name and birth date etc.
First of all you are right the site offered above is not an officail government site. The address for the postal service in Italy is: http://www.poste.it/
As to obtaining your Codice Fiscale "jennabet" said it best. Apply at the Consulate you are registered in AIRE. While the on line generators work they mean nothing unless issued by the government and are not registered in their system.
Look for the form on the Consulate site, fill it in and email it to the Consulate. The NYC Consulate handles the entire process via email.