Where is the post office in newport nc? Newport, NC 28570. The Newport Post Office is located in the state of North Carolina within Carteret County. This location serves 21,432 Newport residents with a median income of $47,356.Is newport in ohio? Census Designated Place in Ohio, United States. Newport is a census-designated place in eastern Newport Township, Washington County, Ohio, United States. Although it is unincorporated, it has a post office, with the ZIP code of 45768. Newport lies along the Ohio River several miles above the county seat of Marietta.What is newport tn? Newport, Tennessee. Newport is a city in and the county seat of Cocke County, Tennessee, United States. The population was 6,945 at the 2010 census, down from 7,242 at the 2000 census. The estimated population in 2014 was 6,880. It is located along the Pigeon River .