Cloudcroft sits on a mountain which overlooks the Tularosa basin. This picture shows the view. The white area is actually White Sands National Monument, one of the largest gypsum dune field in the world.
There are some great hiking trails in and around Cloudcroft. One that isn't too long is called Osha Trail. This hiking trail can be accessed from inside the town or from a parking area right outside of town. It is about 2.6 miles long and a gorgeous hike in the fall. This is how the hike began at the trail head.
Cloudcroft is not far from a solar observatory in Sunspot, NM. If you are ever in the area a visit to Sunspot is a must. The road to Sunspot is a scenic byway and the telescopes are very interesting as well. Here is a big solar telescope at the observatory.