The Roaring Fork motor nature trail is right off the "main drag" in Galtlinburg (turn at traffic light #8) and is very pretty. There are a couple of old cabins you can go inside, and there is a short trail to Grotto Falls. I think even the 5 year olds in your group should be able to do that one. It's really not far, and it's interesting because you go BEHIND the falls when you reach the top. Also there is a shallow pool where you can safely wade. We had fun searching for salamanders in the mud (beside the trail) as we hiked up.
Also, along the drive is a series of waterfalls called the "Place of 1000 drips" that you can see right from your car. You can get out to take pics if you like, but there's no hiking involved.
The hike to Laurel Falls is also very easy (easy as in *paved trail*) but still very pretty. Very nice views.
If you're not up for hiking at all, just drive up to Newfound Gap. In fact, do that anyway. It's spectacular. You can also drive up to Clingman's Dome, but if you want to go all the way up to the observation tower, it's a short (but kind of steep) hike from the parking area. I think my kids were 4 and 6 when we did it, though, and it's paved too.
Go to the ranger station/visitor's center, Sugarlands to watch the 20 minute free video about the park and let your kids see the exhibits. You can also get advice from the rangers about what would be best for your group. There is waterfall out behind the station that you can easily walk to. Flat, very short. Your kids would also enjoy doing the Junior Ranger program. You can pick up the materials in the gift shop there.