La Cueva features 22 miles of hiking trails near Carlsbad, NM.
Go south on standpipe rd. You cross a cattle guard. Shortly after, take a right on a dirt road at the low water crossing. Approx. 1/4 mile down the dirt road there will be a large parking area on your left. Park there.
http://www.tripleblaze.com/trail.php?c=3&i=425