Geologically, the Adams diggings could only be in the southwestern quadrant of the state. Adams himself spent most of the remainder of his life searching the areas in and around Reserve, New Mexico. This area was the largest gold producing area in the state, and hosted several small mining booms, including the rich strikes at Silver City and Pinos Altos. The areas that could conceivably host the diggings in this region (containing several large mountain ranges that remain sparsely inhabited) are numerous, as minerals and evidence of previous mining can be found throughout the area. Local folklore will tell you that the gold is at the headwaters of either the Black River, the Gila River, or the Prieto River. Spanish Lore will tell you to look to the Blue Mountains. Dozens of mining camps in this region of New Mexico were thought to be the Adams diggings for brief periods, until each proved itself to be less rich than at first indicated: egregious hopes followed by rapid disappointment. That seems to be the story of gold in the desert southwest.
