The best museum in Sierra County covers a lot of ground in a relatively small building: Apache history (including Geronimo himself, who camped near the springs), the geology of the region's hot springs, pioneer and cowboy history, and the story of how a small desert town called Hot Springs renamed itself after a radio show in 1950. That last exhibit alone is worth the admission.
The Ralph Edwards Room is a particular curiosity — Edwards was the host of the radio game show "Truth or Consequences," and after the town won his on-air contest by agreeing to change its name, he showed up every year for the Fiesta for decades. The museum has photographs and memorabilia from those annual visits that capture something genuinely odd about mid-century American culture. There is also a replica of an Apache wickiup outside and a good collection of Mimbres pottery.
story: "In 1950, radio host Ralph Edwards offered to broadcast his show live from any American town that renamed itself Truth or Consequences. Hot Springs, New Mexico took the bet — and Edwards kept coming back for their annual Fiesta for over 50 years."