We're finally going to take the bull by the horns and go camping with our kids. We're thinking of visiting the mountainous area in West Virginia. I understand they have lots of wilderness, animal-oriented parks and attractions suitable for children. Call me brave papa.
Don't overlook some of the areas in East Tennessee as well. The Great Smoky Mountains National Park, Big South Fork, and a whole assortment of state parks in the area to choose from. I don't know where you're located, but East TN is like hiking/camping central.
If you have pets, Big South Fork is a good option. They allow dogs on the trails if I remember correctly.
If you decide to bail on it, you could always drive on over to Gatlinburg/Pigeon Forge and play putt-putt golf, ride go-carts, etc.