Before you get to Carlsbad you might want to make a stop at Benson, AZ just east of Tucson and tour Kartchner Caverns in the state park. It's altogether different from Carlsbad in that it still a living, growing cavern. The tour is awesome and the caverns gorgeous with nice lighting. It also has a wonderful campground with big lush sites....lush for a desert. :)
Carlsbad is worth it but it's neat to compare the two. Nearby you could also tour Bisbee and definitely take the underground mine tour. Also nearby is Tombstone and Chirichuha Nat'l Monument and the rock formations are very unique.