We have some great options here...from easy to hard with a little of everything in between!!!
Most everything around involves a climb or two which seems to be most kids downfall (most of the easy to moderate trails the youngin's just roll right through)
There is Bent Creek close to downtown Asheville which has camping, lake, and numerous trails dubbed easy by the locals...it is our weekday spot! We can do from 1 hour to 3-4 hours depending on mood and schedule.
If you are looking for more "out in the woods but with conveniences" I would stick to your original plan of Bryson City area...you will be close to hiking, biking, lake, whitewater, and various ammenities if you don't feel like camp food. Also if you are not wanting to "tent" it then look into camping cabins...I know some people who stayed here and said is was nice yet still rugged feeling....
http://www.tumblingwaters.com/
Fontana Village is a bit more crowded (but city it is NOT) it has a lodge, cabins, bike shop, rec room, trails...pretty much all in one spot! You could most likely leave the car in park the whole time!
http://www.fontanavillage.com/
Dupont is also a great area...near Brevard (home of the White Squirrel) it has a "kids trail" which I have yet to check out. If you do look into this area please, PLEASE whatever you do...DO NOT stay at Ultimate Ride Campgrounds...they have not been very friendly from what I have heard ***not personal experience.
Feel free to PM me anytime...I work in front of this glowing box all day so I get emails ALL DAY LONG!!!
have fun planning....



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