The short answer
A Santa Fe hot springs trip has one decision hiding inside it: do you want a Santa Fe weekend with one spa session, or do you want the hot springs to be the lodging experience? Ten Thousand Waves is the closest and most polished answer, but it is a Japanese-style spa with treated mineral water rather than a natural geothermal spring.
If you want the room, dinner, and soak in one place, book Houses of the Moon at Ten Thousand Waves. If you want Santa Fe first, stay around the Plaza and reserve a private tub. If the words natural mineral water are the point of the trip, compare Ojo Caliente before you book anything in town.