Consider Yellowstone. So much to see and do. There are Ranger programs for the kids, you can take a covered wagon trip to a cookout, many lodging choices with a pool and there's always the lake if you enjoy freezing water. You can take a boat ride, some easy hikes, what child wouldn't enjoy the geysers? Or the other fascinating geological formations? Or the bison walking across the road?

My daughter was four the first time we went, and she loved it. You don't have to be "outdoorsy" to have a great time.