If you are going to the Smokies, check out the elk herd at Cataloochee Valley which is right off I-40 .. also has a lot of old buildings that the park service took over. Not too far from there is Maggie Valley and there is a great motorcycle museum called Wheels though time.
Asheville N.C. is one of the loveliest cities anywhere. You already have a nice itinerary picked out. I would suggest a leisurely drive up the Blue Ridge Parkway to at least Blowing Rock. The scenery is mind numbing and Blowing Rock is a quaint and fun town to visit. May, might be just a bit early for the "fire on the mountain" Azalea bloom, depends on the weather.
You've pretty well got the immediate Asheville area covered with your list. Maybe add the Folk Art Center (on BRP near US 70 on the east side of town).
I'd add a day (or two) on the the Blue Ridge Parkway. If just one, and a clear day, go north to Mt. Mitchell (highest peak east of the Miss.). Walk up the fairly short & steep but paved trail to the overlook tower at the top. Take a full tank of gas & maybe lunch. There's a usually-mediocre restaurant in MM state park; snack bar at the upper parking lot there has good prices but limited selection). Coming back on the P'way, stop at the first Craggy Gardens parking area (north side of the tunnel and visitors' ctr) and take the 3/4 mi. hike up to Craggy Pinnacle. Unpaved, eroded, rocky trail to a grand 360 view.
If you've got two days (or are willing to make a long day of it) to do the BRP, go south/west past A'ville. Go past Mt Pisgah, and the scenery gets quite spectacular from the roadway. You can go this way to get to the Smokys, but it's going to eat into your time.
With 2-way drive time, you'll have a long day to see the Smokys from an Asheville base, but it can be done as long as you don't linger too long in Cherokee (native word for 'mostly tacky tourist trap'). If mtn 2-lane roads don't bother you and you're not towing, the best route is I-40W to exit 27; follow the signs for US 19 thru Maggie Valley over Soco Gap and down into Cherokee, then US 441 thru the park. Alternately, stay with US 23-74 over Balsam Gap to Dillsboro and on to Cherokee on US 74-441 (good 4-lane, somewhat longer).
"The" scenic hike in the Smokys is Clingman's Dome. A stiff uphill ~1/2 mile walk on a paved walk will take you to the observation deck, another 360 view.
Jim, "Last night as I lay in bed I wondered, 'Where the heck is the ceiling?'"
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..As a picture suggested, the Biltmore House is a must...looks like a castle...beautiful grounds...your not very far from Maggie Valley or Cherokee...as mentioned the Parkway can be accessed in more than several places around Asheville...Mt. Mitchell, highest mountain east of the Mississippi is about a little over an hours drive from Asheville. You also have a very large Farmers Market in Asheville and a ton of resaturants to choose from...I hit a few of the places you might want to go to, you also have Lake Lure and Chimney Rock that is about a 45 min. drive from Asheville...the scenery is awesome.
Jim & Kathy
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