We have stayed at Brookside (
http://brooksiderafting.com/) and had a stream side campsite with the grandkids...not really for fishing, but plenty to stay cool in, and lots within walking distance to explore, and then there is the rafting. There are no campgrounds on Lake Nantahala (that I have seen), but there is public access for fishing.
Someone already mentioned Deep Creek Campground in Bryson City...they stay booked up, but have nice creek side campsites if you can get in...and then there is the Deep Creek campground just inside the park boundary, but not sure if it is open...Deep Creek is one of the best kid friendly tubing places around.
If you don't mind driving a little further, I would recommend looking around Santeetlah Lake near Robbinsville...beautiful area, and we stayed there a number of years ago in the campground at Cheoah Point Rec Area, but I think it may have fell victim to the great COVID panic of 2020...you can search online and see if there are other camping options around Santeetlah...if you have a small boat, trolling for Walleye here was great (or it was when I was there 15 or so years ago).
Oh, and take the kids for a walk through The Joyce Kilmer Memorial Forest...the largest trees in North America outside of the California Redwoods are here...the largest tract of virgin eastern north American forest left....will make you feel like a hobbit, size-wise anyways.
If my wife would ever agree to move, I would live out there...
oh, and don't forget...Great Smoky Mountains is one of the Missing 411 hotspots...
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