Locate a post office ("Correos de Mexico") and mail your postcards from there. Don´t forget adequate postage (stamps). You can also ask in your hotel whether they offer a postal service. Be aware that it may take a while for them to be delivered, especially if they are sent overseas.
If you are sending a package from Mexico, be prepared to open the box for inspection. For better and faster service, use international couriers such as UPS, Federal Express, or Estafeta. They will be more expensive but more reliable.