There is plenty to do down there.
Elephant Butte Lake for swimming, boating, jetskiing
Alamogordo for wineries and pistachio groves, skiing up in Cloudcroft/Ruidoso area
Casino over in Ruidoso
White Sands NM - my favorite place on earth
Carlsbad Caverns
Relatively easy drive up to Alb area for shopping and more cultural/outdoors stuff
Grab a trip guide to NM. I recommend Frommer's.
All driving there is pretty easy as the roads are nice and flat (for the most part) and speed limit is between 65 and 75 for many highways.
And enjoy! Coming from NJ you are going to love the prices in NM.