The Atlantic
Atlantic Ocean
5km east
Iran is due east of Iraq.
The country due east of Jamaica is Haiti.
Kansas is due east of Colorado and due north of Oklahoma.
If the star is observed rising due east in the US, 6 hours later it will have moved to 90 degrees to the west, or due south. It will continue its apparent motion across the sky, following the arc caused by the Earth's rotation.
The direction of a vector pointing due north is measured in degrees clockwise from the north, with 0° being due north. The direction of a vector pointing due east is measured in degrees counterclockwise from the east, with 0° being due east.
East is a direction, a compass point. To the right on a map held the right side up. "due" wrt directions means "straight". So "due east" means "straight (to) the east".
The sun only rises in the due East during the equinox. At that time it rises in the due East everywhere on Earth except at the poles which have no east.
The country that is due east of Florida is the Bahamas.
Portugal is due east of New York