North Carolina, with its coast on the Atlantic and its Western Tip in the Appalachians, hosts the famous and busy Great Smoky Mountains National Park. South of this park lies the Nantahala National Forest. And north is the Pisgah National Forest. You will find some 2000 miles of trails in these areas.
The Appalachian Trail goes through the heart of the Great Smoky Mountains. The Mountains-to-Sea Trail will take you (when it is ready) from the Great Smoky Mountains to the Croatan National Forest and Cape Hatteras National Seashore, some 900 miles.
Interesting is the 300 mile Benton MacKaye Trail, in the remote backcountry of North Carolina, Georgia and Tennesse.
The long East Coast Greenway and Eastern Continental Trail also cross the state.