The question contains a misconception: there is no single "Museum of Anthropology" in New Mexico. However, the state hosts three notable anthropology-focused institutions:
University of New Mexico's flagship anthropology museum. Collections: Southwestern archaeology (Ancestral Pueblo, Mogollon), ethnology (Native American, Hispanic), osteology, and archives. Famous for the "People of the Southwest" exhibit and the Hibben Center for Archaeological Research.
Part of the Museum of New Mexico system. Focus: Native American cultures of the Southwest—pottery, textiles, jewelry, baskets, contemporary art. The Laboratory of Anthropology holds vast research collections.
Eastern New Mexico University. Showcases the Clovis type site (13,000-year-old Paleoindian culture) with artifacts, stratigraphy exhibits, and active research.
If you're seeking a specific Pre-Columbian relic, identify which museum holds it—each has distinct strengths. The Maxwell is likely the closest to a general "Museum of Anthropology."