Which city was established as the capital of New Mexico?

Santa Fe was established as the capital of New Mexico in 1610, making it one of the oldest cities in the United States and the oldest continuously inhabited state capital. The city's strategic location and cultural significance as a trading and religious center for both Native Americans and Spanish colonizers contributed to its designation as the capital.

St. Augustine, founded in 1565, is notable for being the oldest continuously inhabited European-established settlement in the continental United States but was not associated with New Mexico. San Diego and Los Angeles are significant cities in California but do not have historical ties to New Mexico's governance or capital status. Santa Fe's rich history and its role in the governance of New Mexico distinguish it clearly as the correct answer.