Having lived and worked in the area for some years, I have a suggestion for your consideration. Use Maggie Valley as a base. When you get to Spartanburg, hire a car and head north to Hendersonville. Hopefully, you will be in Spartanburg in the morning. You'll use a lot of daylight driving. Turn west at Hendersonville, through the mountains to Waynesville and go past there to Maggie Valley. See attached map.
You will have driven enough mountain roads that lesser challenges will be welcome on the next days. Note: the roads are good, well paved and safe but lots of curves. Great views. However, in April, the leaves will be just starting to bloom. Use Maggie Valley as your home base. A few "day trips" from there, will give you the feel of the Smokey Mountains and the Blue Ridge Highway.
One trip is west to Gatlinburg, TN (not that far. Easy drive). The ski slopes will likely be closed, as it's past time for snow but that community is designed for fun. Lots of art. That trip would be all day.
Another day: Nearby is Lake Junaluska. This is at a lower elevation. The Dogwood Trees should be in bloom. Frame the lake with white and pink flowers. Lots of waterfowl. Winner photography. Continuing on, Ashville. Stop by the Biltmore House. Massive mansion. Opulence and history. Also, the many, many creeks and waterfalls will keep you clicking. Buy local maps. Look for streams and parks.
Another direction from Maggie Valley will take you to Indian Country. Cherokee is somewhat commercialized but fun. The drive is short and pretty.
Your task is to Google all the obvious words above. Maggie Valley is very unique and warmly inviting.
Here's your first map:
https://www.google.com/maps/place/Great+Smoky+Mountains+National+Park/@35.3119943,-83.4030275,9z/data=!4m2!3m1!1s0x0:0x3c926fc1a7752461
Maggie Valley:
https://www.google.com/search?q=maggie+valley+nc&ie=utf-8&oe=utf-8Others will make suggestions. You've picked a great area with lots of beauty and fun. #1 most visited National Park (like Crowne Land [I was a teacher for 3 years in NSW]). You've got lots of time to pick and chose. Whatever you choose, "she'll be right mate, fair dinkum."
Final note: if this is your first time not driving on the wrong side of the road (making joke), look both ways, at least twice. Be safe. When pulling out on a road, if there is no other vehicular traffic, it's easy to fall back on old habits and drive on the wrong side. I know! Be careful.