You can have "VETERAN" printed on your North Carolina driver license or ID card as proof of service. Adding the designation is free, though the normal renewal or duplicate fee still applies.
Go to any North Carolina Division of Motor Vehicles driver license office and ask for the veteran designation.
One of these as proof of an honorable discharge: a DD214 or DD215 certificate of release or discharge, a WD AGO 53/55 report of separation, a NAVMC 78-PD notice of separation, or a NAVPERS separation of service.