There is a place not too far away called Grandfather Mountain:
Grandfather Mountain
It's a BEAUTIFUL place to camp/hike, etc... absolutely beautiful..and some of the trails are fine for pets..but there are others for more experienced hikers that are VERY difficult. I went on one where it literally took another person or so to help you climb, etc... one person had their dog before knowing how tough it was. At one point it was pretty dangerous we had to use a few people and left the dog to a safe location during the hike. It could have easily been fatal for the pooch if people had not been around to help the dog out. It gets pretty rough there...
While generally hiking is pretty safe..some places do have some rough terrain and it's just safer to leave the pets at home and bring them on easier trails. I love bringing my dogs hiking but I also want them to be safe!