Lees-McRae College and the popular ski resort town of Banner Elk are located in the western part of this state. One city in this state is home to the historic Grove Park Inn, and that city is also home to the largest house in the United States, the Biltmore Estate. The eastern part of this state includes the towns of New Bern and Smithfield, and a popular tourist destination in this state is located in a region which includes Cape Lookout and Bird Island. In addition to 
Lees-McRae College and the popular ski resort town of Banner Elk are located in the western part of this state. One city in this state is home to the historic Grove Park Inn, and that city is also home to the largest house in the United States, the Biltmore Estate. The eastern part of this state includes the towns of New Bern and Smithfield, and a popular tourist destination in this state is located in a region which includes Cape Lookout and Bird Island. In addition to Cape Hatteras, the capital of this state is part of the "Research Triangle" with two other cities, one of which is home to Duke University. For 10 points, identify this state which is home to the cities of Asheville, Durham, and capital Raleigh.
Lees-McRae College and the popular ski resort town of Banner Elk are located in the western part of this state.
{North Carolina}