The first thing you can do is enjoy a sunset on what are arguably the most scenic mountains in New Mexico, the chisled Organ range.
You are only an hour's drive from the famous White Sands National Monument, just west of Alamogordo, and through the Organ Mountains. (Don't expect lush forests.here)
What is in reality white gypsum deposits blown into sixty-foot dunes, the White
Sands provide a very impressive and unique siight. Mornings are best, because it can be over 90F. by mid-afternoon. Bring water to take into the monument...there is none in it's interior. (Enttrance to middle picnic area is about 9 miles...driving on hardened white gypsum....cool!
The Space Museum in Alamogordo is interesting, and if you'd care to drive east from Alamogordo, you will climb up to the little village of Cloudcroft, so named because in certain conditions the bottoms of the clouds actually do touch the pine forests that surround the town. Elevation is just under 9,000ft, and the short drive, on an excellent U.S. highway, will also take you through New Mexico's only automobile tunnel, cut through about 100ft of solid rock.
Cloudcroft is a quaint little place, and you'd be well-advised to grab a lunch to go, and head for some of the many picnic areas in the national forest surrounding it. There are several motels, and some cabins (if available) in the town if you would care to spend the night. (It would only be a couple of hours back to Las Cruces directly.) If you stay...drive the highway south out of Cloudcroft to the Sunspot Observatory...this road will provide you the best chance to see some wild Mule Deer (larger than the White Tails of the East), or possibly the more elusive Elk, just before sunset...35-40mph max.
Take in Old Mesilla, a picturesque little adobe village just 3 miles south of Las Cruces. Many shops and some of the area's best New Mexican Restauants. (La Posta Restaurant has been around for years... and years. Great ambiance with your meal.)
This one and a half day side trip to Cloudcroft should prove enriching for you. Keep in mind that Southern New Mexico is in a true "Low Desert" region, while Northern New Mexico (north of Albuquerque and I-40), is "High Desert" with more forested mountains, mesas, and flora. Please return again to take in the more scenic areas of the state. (Southern New Mexicans may send their letters of disagreement to me at...! LOL)
Please do not think of a side trip to Juarez, across from El Paso. Bagdad is probably a safer place today. "Thousands" of people, including wayward Americans, have been killed over there in the ongoing drug wars. El Paso on the other hand is a very safe city, with low crime rate.
Enjoy your trip!