You get an amazing view of the Organ Mountains looking east from almost anywhere in Las Cruces, New Mexico. But wait until you travel out of town, up Highway 70, over the pass and find your way to Aguirre Spring Campground!
I've never stopped at the visitor center. Unless you plan on camping, there is no need to as the major stops all have an honor system area to pay $5 for a day pass. My favorite among these stops is Pine Tree Trail. This 5-6 mile loop offers great, moderate-level hiking with easy to find trails and increasingly amazing views as you make your way up to the midpoint. At this apex, you can take in White Sands Missile Range facilities and further off, a squint eyed view of White Sands National Monument.
More to the point, the loop offers plenty of nature-viewing, from old pine to deciduous, leafy woods in the wetter areas, and plenty of rock viewing. Take a look at the majestic Organs from the other side, Las Cruces!