One of the world's largest solar observatories is near Sunspot, 20 miles south of Cloudcroft. Though it's primarily for scientists, tourists can enter the visitor center, walk through the observatory (when staffed) and follow a short walking-tour path around the grounds. The high and beautiful Sunspot Scenic Byway leads to the site, with the mountains to the east and White Sands to the west. From Cloudcroft, take Hwy 130 to Hwy 6563. Fill your tank before you set off.
The Dunn Solar Telescope is open to the public when in use, typically on weekday mornings. Guided tours are offered from June through August at 2pm Friday through Monday.
A scale model of our solar system, with signs noting the location of each planet (or former planet), begins with Pluto at the Chamber of Commerce Visitor Center, continues along NM 6563 and ends with the sun at the observatory. There is no Uranus sign because people keep stealing it!