The short answer
Hot Springs, North Carolina is a lodging decision first because the resort experience is private tubs, not a big public swimming pool. If the mineral bath is the reason for the trip, stay at or very near Hot Springs Resort and Spa. If the town, trail, river, and mountain weekend matter more, use town lodging or Asheville as the wider base.
The operator's current pages describe private mineral baths open to the public by reservation, with standard unjetted baths and deluxe or signature jetted options. The accommodations page also notes a two-night minimum for overnight stays and a campground repair note after Hurricane Helene, so verify specific lodging categories before making the campground part of the plan.