http://www.kentuckytourism.com/big-south-fork-scenic-railway/2248/
I've done this several times, and always enjoyed it. There is also some breathtaking scenery along the hiking trails in Big South Fork. Nearby Pickett State Park is pretty also.
My family has always enjoyed a weekend trip to any of our state parks; especially the ones with Inns on the grounds. Hiking, canoeing, fishing, swimming, playing ball, trap shooting, biking, etc. are a few of the things we've enjoyed at Montgomery Bell, Fall Creek Falls, Henry Horton, and others. There are always park rangers there with various activities for the kids. I've enjoyed many of these as well.
We always have a great time in Chattanooga as well. The aquarium is great. There are a lot of good restaurants and things to do near it. Lake Winnie is great as well. It's like you stepped back in time about 50 years. A lot of history is on display in Chattanooga. Just stay in the touristy parts and don't venture too far off the beaten trail. My wife still fusses about the Holmes Wrecker Body Museum, but I thought it was interesting.
I'm out on Gatlinburg/Pigeon Forge. It's a giant traffic jam/money grab/tourist trap.