First of all, the Blue Ridge Parkway does not go through West Virginia, so if you want to go there it won't be part of the BRP trip. The BRP lies in Virginia and North Carolina. How much time do you have? If you want to travel the entire length of the Parkway, you could easily spend a full week doing so. Or you can spend as little as an hour or two and get some very nice scenery along with a couple of interesting stops. Let us know a bit more about your schedule and we'll be glad to help plan your itenerary.
I will mention a few things: First, I assume you'll be coming down I-77, which does take you through West Virginia on your way to NC. I-77 intersects the BRP about halfway down its length, so you may want to get on there (at Fancy Gap, VA) and take it into NC towards Boone.
Probably the most popular section of the parkway is between Boone/Blowing Rock and Asheville. This would take about 2 hours if you drove non-stop, but it's better to plan at least a day so you can take a leisurely trip and stop at the many sites along the way. You can find plenty of cabin rentals in either Boone/Blowing Rock or Asheville.
You may also have the option of coming down I-75 from Cincinnati through Kentucky to Knoxville, TN, then taking I-40 east into Asheville--depending on where you're coming from this may be a better alternative. If that works better for you, it might make more sense to explore the southernmost section of the BRP, including the Great Smoky Mountains National Park, and ending up in Asheville. Or you could proceed directly to Asheville via I-40 and then work your way north on the BRP to Boone/Blowing Rock.
Finally, you didn't say when you plan to come, but be aware that during the winter months some sections of the parkway will be closed due to ice and snow. Here are a couple of links to information about the BRP that should help with your planning, including information on closures:
Maybe one of the above suggestions will help you find what you are looking for. March 18-22 will probably still be chilly weather.
According to the BRP.org website, a section near Craggy Gardens will be closed until April for landslide repair. Otherwise, the closures depend on the weather.
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