Take 'em up to Max Patch! Perfect time of year for it.
me
My 2-year old walked up to the top by herself, but since it is along the AT, there's also opportunity for longer hiking. Me and the kids like to hike it barefoot. It's a huge grassy bald with 360 degree views of all the nearby mountain ranges, including the Smokies and Blacks. Take a picnic for sure.

The drive up there is beautiful ... Spring Creek Gorge, mountain viewis, etc.

Paint Creek is pretty cool too. Just go downstream from Hot Springs several miles on the road that hugs the banks of the FB. Nice little creek with some neat waterfalls and swimming holes.

Opportunities are endless, but those are a couple kid-friendly things that come to mind.
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