West Virginia is simply a hiker's dream. They don't call it the Mountain State for nothing. There are great hikes, short and long, steep and flat, seemingly everywhere. I already mentioned the rail trails in other posts. Portions of the Appalachian Trail meander through the state, as well. Chances are, if you visit any city or town in West Virginia, there should be some hikes in or around the vicinity. If you have the time to really explore the state, then you will find more remote trails to venture on than you will likely be able to do in a lifetime.
My $.02 on hiking is that it is cheap and healthy, and really forces you to slow down and take in the sights and be with the environment the way nature intended. In a time and society when we are constantly in a rush to make the next buck, buy the next gadget, and be thrilled and entertained, a walk in the woods may seem underwhelming to families, particularly youngsters. But it doesn't have to be that way, as long people are willing to try to slow down their pace every once in a while and take in, really take in their surroundings. Go on hikes with your family, and find out just how amazing walking, just walking, can be for the mind and body.
Perhaps one of the best parts about hiking is all that you don't need to do it. Just some sturdy shoes and appropriate clothes for the climate should do it. In most cases, running shoes are fine. No expensive gear, unless you are going backpacking. It's a very cheap and healthy family activity. You can reconnect with each other. There are no distractions. It is fun simplified. There are plenty of trails, guides, and info out there. You don't have to climb Whitney or complete the Appalachian Trail. Just find a nice trail close by, and let it take you.
I recommend an excellent set of books by WV native Leonard M. Adkins for tons of info on hiking and exploring the Mountain State.
50 Hikes in West Virginia
West Virginia - An explorer's guide series