You should search the forums on this, there are quite a few threads on things to do in Gatlinburg.
I like to go into the National Park. There are a lot of short hikes that are good/easy for families. I love the Grotto Falls hike out of Roaring Forks nature trail (the nature trail is nice, it is a one-way loop that you drive and has lots of neat stuff, out of Gatlinburg. Turn at traffic light #8 to get to it). The falls hike is nice, about 3mi round trip and you can walk behind the falls. If you go on Wednesday you can see the llama train that supplies LeConte Lodge.
If you go into the National Park itself, there is Sugarlands visitor center as you come into the park, on your right. There are a lot of short nature walks, some ranger led and some not, that are out of here, plus lots of info on the parks. turn right there and head up to Laurel Falls, a nice paved hike but usually super busy. Hold onto your kids at the top because the trail comes out at the top of the falls. Just beyond Laurel to the left is Elkmont campground and Jake's Creek, there are old cabins and Ogle cemetary up there, a few nice walks along Jakes Creek. Continue on past Elkmont and you will eventually get to Cades Cove which has loads of stuff to do. You can drive or bike the loop, they have hayrides some evenings, a ton of hikes, old cabins, etc.
Instead of turning right at the visitor center, if you continue straight you can go to the Chimney Top campground, it is a nice spot to stop and grill out or have a picnic. If you go at dusk you can usually see black bear here (you will also see them in Cades Cove). Carry on up the mountain and you can stop at Newfound Gap, which is where NC and TN line is, and there's a nice hike up to Clingman's Dome just past that, which is the highest point in the park and gives great views on a clear day.
All of that is free - you've already paid for it with your taxes. It is also my favorite place in the world.
In Gatlinburg proper, the aquarium is worth the admission ticket. I actually like to ride the sky ride up the mountain, it is cheesy and sort of expensive, but you do get nice views. I would stay away from anything with Ripley on it except for the aquarium, tourist trappy. My kids like the Hillbilly Golf at the entrance to Gatlinburg. In Pigeon Forge, Dollywood is actually surprisingly nice. I'd rather stay up in the parks though.
Have fun!