If you Go to the New River, take the road through the gorge. It's well worth it.
I'm generally not a fan of going to National parks. I prefer to be less restricted in what I can do.
I live next to The Great Smokey Mountain NP, I hardly ever go to it because I can go to the Cherokee NF which has most of the same features but I can get away from the crowds of people.
In the park, there are many trailheads near Gatlinburg that have never been sized for the amount of traffic they get, BUT somehow they found money to pave the trail. I do not find it fun to hike with hundreds of other people in hearing distance.