Does your family hike? My wife and I hiked all over the Smokies, we started by hiking to every waterfall in the park, then most every bald, then Mt Le cont twice from different directions , the Chimneys and a bunch of other places I can't remember.
A couple of nice walks near Elkmont, two waterfalls, one back toward Gatlinburg and not far from Elkmont and one in Cades Cove.
Best time to go to Cades cove is about 5:00pm when the critters are starting to stir and coming off the ridges down into the fields.