As in practically all of the South, sweet iced tea is the beverage of choice for a lot of people; the stronger and sweeter, the better. "Iced" is always assumed ask for "hot tea" if you want it steaming and "sweet" is the default, although people still tend to specify "sweet tea" when ordering. Most places do offer "unsweet" tea, but remember to ask for it if you want it.
In almost all of the incorporated towns of Carteret County, restaurants with Alcohol Beverage Control ABC permits are allowed to serve mixed drinks; the exception is Newport, which - along with the unincorporated areas of the county, including Down East - will only serve you beer and wine. If you want to purchase your own alcohol, beer and wine are commonly available in stores, but liquor can only be purchased at an ABC store, open Monday through Saturday.