You would actually be closer to 5 1/2 hours from the Asheville area. You would be in the range of 6 1/2 to 7 1/2 hours from the Gatlinburg area. There are roads, depending on the time of the year ie. no snow, that you can take from I-40 once you cross into Tennessee that allow you to "back door" into the Gatlinburg area.
Obviously, you can get off of I-40 at several points in NC and do lots of touring of the Smokies. It is not close to the Smokies from HH. I am sure that there are other folks who know more about other "mountains" closer to the HH area. I grew up in Knoxville, Tn and we went to the Smokies before it was "popular" and enjoyed the streams, hiking, picnicing, swimming, etc.; the only problem is that we did out of Knoxville so I don't know as much travelling up from HH. I did live in Charlotte, NC for a few years and actually did backdoor into the mountains off of I-40 a few times. Good luck in finding what you are looking for. HH is a great resort....it is our home resort. We are headed there in May...we love it. It is a great place for a family with little ones.
