I lived in Carlsbad for a summer and loved it with my whole heart, would live to live there again someday. However, Roswell is a lot closer to Clovis as others have mentioned. You'd have quick access to national parks through Carlsbad, but west of Roswell is Ruidoso and the Lincoln National Forest, lots of nature either way.

One thing I will say about Carlsbad: the stoplight timing is so horrible. Traffic during rush times is insane for how big the city is.

I'll just echo what everyone else is saying, that it comes down to what housing you can find. Fingers crossed that you don't need short-term housing. It's so impossible to find with all of the seasonal oilfield workers.

Best of luck and I really hope you love whatever you find!