There are some excellent reference books to hot springs, both wild and commercialized. I believe this is a book I had, and if so quite good:
Amazon.com: Hot Springs and Hot Pools of the Southwest: Jayson Loam's Original Guide (Hot Springs & Hot Pools of the S Jayson Loam's): Marjorie Gersh-Young: Books
There is a sister book which covers the northwest US.
Haven't been to most of these, unfortunately, although it would make an interesting quest.
A commercialized hot spring with a great source of natural water is at Ojo Caliente, NM:
Hot Springs, New Mexico - Ojo Caliente Mineral Springs Resort and Spa
A laid back place with pleasant ambience. Quite nurturing. Lovely setting as well. The day long admission price is relatively modest. They have a series of different pools, each different in character and type of water. Something unique at this location as one can so easily choose which types of minerals to soak in. You'll meet an eclectic mix of people from all over the globe. Particularly mid-week or off season it can be quite mellow. I should go back.
There are two natural hot springs in the Rio Grande river canyon just outside of Taos, NM, so close to the river that they flood come spring. Both a favorite of locals. Somewhat remote. Clothing optional. The more public of the two is located on the west bank of the river, accessed via a relatively short trail leading from the first hairpin turn of the dirt road after crossing the bridge over the river. Turn off NM 522 at Arroyo Hondo, NM.
The more private and sedate of these two springs is on the east side of the river, a couple miles or so below the other spring. It is best accessed via US 64, turning on, as I recall, Tune Dr. (a good dirt road) near where one leaves the last vestiges of 'civilization' but before crossing the Gorge Bridge across the Rio Grande river. From there about 5 miles until reaching the parking area and trail head at the edge of the canyon. A foot trail leads downriver from there a little over a mile (about) to the springs at the edge of the river.
Both these springs issue from the ground at about 97 degrees fahrenheit, which proves to be a nearly perfect temperature. One can soak near indefinitely, even in winter with snow falling on your head. Only problem then is the brief chill on emerging and before being snugly dressed once more. There are no services or facilities at either spring. The pools are somewhat different too, with basically just one fairly large one at Black Rock (on west side) and the choice of several (with different temperatures) at Stagecoach (east side).
If you go please respect these springs. Not everyone does, particularly at the more easily accessed and public Black Rock. Stagecoach tends to attract the more serious and respectful nature lover. They are indeed a gift. Haven't been in several years so circumstances may have changed, but suspect not much. When there in the water, within this canyon, it can seem as if the larger world without doesn't even exist. With the right mood, surreal.