Nick
You will be here during turkey season which normally runs from April 15-May 10. There are lots of birds in the Sacremento Mountains. If you are living at White Sands it will be about an hour drive.
I actully have an oryx tag on White Sands Missle Range for March. You may have heard about our local oryx herd. You will see many of them if you spend any time on the range. They live from the Texas line to about 100 miles North, mosly in the Tularosa Basin, but also on the Rio Grande side of the San Andreas Mountains.
March is kind of the end of the coyote season, although you can hunt them year around. We have lots of coyotes, if you can just find a day in March when it is not windy.
As far as shoots go I am out of the loop anymore. We use to have many local shoots all spring and summer, but that was 10 years ago. It would not be hard to find out if there are any shoots going on.
I think you will find it to be an interesting area.
Patrick