New Mexico has 33 counties, which each have their own trial courts. The New Mexico Appeals Court reviews the decisions of those lower courts. If further appellate review is desired it is handled by the Supreme Court of New Mexico.
The three largest municipalities in New Mexico are Albuquerque, Las Cruces, and Rio Rancho.
Any complaints regarding the competency or ethics of your attorney should be made with the Disciplinary Board of the New Mexico Supreme Court. To report an attorney mail a New Mexico Complaint Form to P.O. Box 1809, Albuquerque, New Mexico 87103-1809.