I would recommend against northern NM, especially the Pecos, in March. The elevations are high, so that means snow and lots of it. the weather could be good in March, but unless you are planning a snowshoe/ski winter camping trip I would go back to the southern ranges. The Gila is huge, so I'm sure you can find something different than last year. Depending on how many days and how far you want to go, I would suggest starting up Turkey Creek and hitting the hotsprings there and then exploring the SW corner of the Gila wilderness. Not too crowded and beautiful loops can be done.
Also, this year's El Nino is hitting New Mexico pretty hard, which is great for skiers, but poor for shoulder season backpacking.