I think you just described most of West Virginia.
Try some of these:
That's the New River Gorge National River site. Check out the webcam; IIRC, it's on the visitors' center porch. There are some river detours going on because of bridge work, but there's still rafting on the river and you can railfan from incredible heights.
I second the recommendation for an Elkins-based trip, because you can get to so much from there.
Should you come down from the north on your way in, Tygart Lake is worth a look near Grafton. The old B&O in the town itself isn't as active as it was in its glory days, but the park and lake are beautiful and the little visitors' center is worth seeing:
Elkins has chain motels, fast food and all the usual resupply stops. If you're into Civil War history, there's a surprising amount nearby. For that, you can try
Should you travel down the Kanawha River, you might like the look of the Great Falls. If you do go that way, you could make a side trip to the railroad museum in Huntington. There's a lot of river traffic between Charleston and the mouth of the Kanawha. You might enjoy a picnic at a lock and dam either there or on the Ohio, and either way you'll be near active rail lines.
Gabe is pointing out that Google Earth is a good resource to get an idea of the kind of territory you'll see. He also reminds me that if you're used to having a lot of convenience stores and such around, you may be a tad alarmed at the distance between food and fuel stops and you'll do well to start out in the morning with a full tank and extra snacks. Most people are friendly and won't mind giving you directions if you need them. GPS isn't always reliable. Also, the National Radio Quiet Zone means your cell won't work around Cass except for 911. (By the way, do stop and see the National Radio Astronomy Observatory if you have time.)
Late September weather in the mountains can be anything from a hurricane passing through to hot and dry to cool and beginning to flurry at high altitudes. It's best to check just before you take off and adjust accordingly, but in general, take at least a light jacket with you even if you can't imagine needing it.
Originally Posted by laming:
We love to view waterfalls and white water, as well as bluffs and such as that. We also enjoy historic small towns, mountain vista scenes... just about anything to do with mountains, small towns, and steam trains!