It sounds as if you already have the place to stay, and are looking for attractions.
If you're in the Asheville area, by all means visit Biltmore Estate, the largest private home ever built in North America. Take time for the winery and the farm as well as touring the mansion.
If you're a fan of Billy Graham, stop by The Cove, just an exit east of Biltmore.
Chimney Rock and Lake Lure are near Asheville. If you go with your RV, do not take the road directly from Asheville. I did that, and wouldn't recommend it to my worst enemy (but if he had an RV, then I might. Take I-26 east to the Bat Cave exit and go north from there.
Spend some time on the Blue Ridge Parkway, and go south to Cherokee and through the Great Smokies National Park. Get a Parkway directory, or check it out on America's Byways®: National Scenic Byways Online
to get information about some of the attractions there, like Grandfather Mountain, Lynn Cove Viaduct, Linville Falls, and more.
Have a great time.