Following the union of Aragon and Castile in 1479, along with the contemporaneous influx of American gold and silver, Spain began issuing the excelente (gold) and the real (sliver -- the famous piece of eight being eight reales in weight). The piece of eight, or Spanish dollar, in competition with the German Thaler, did not become common until Charles I in the early 1500s, but had won basically universal acceptance by the 17th and 18th centuries.

The conquistadores would have used native coin from Spain until mints were established, chiefly in Peru and Mexico, in the 16th century. Areas rich in metals in Mexico were Zacatecas, Guanajuato, Pachuca, Taxco, and San Luis Potosi. Peru accounted for 2/3 of precious metals output of the Spanish colonies after c. 1675.

Sources: 1965 Encyclopaedia Britannica; 1968 Langer's Encyclopedia of World History.

The corollary is that, given the popularity of the coin and the proximity of Latin American mints coupled with the attitude of Britain toward the colonies, the popularity and legal acceptance of Spanish coin in the Colonies and later U.S. into the mid 19th century is easily understood.

Edit: And since my dead-trees library is oriented more toward ancient history, I could cheat and go to Wikipedia, where there is a page with lots more details on Spanish American coinage and mints

Edit++: Actually, some more info was there in Britannica, and I needn't have cheated at all: the first Mexican mint operated continuously from 1535 until 1821; Potosi c. 1574-1825. Other minor mints included: Santo Domingo (1542), Lima (1568), Santa Fe de Bogota (1626), Guatemala (1731), Santiago de Chile (1749), Popayan (1732), and Cuzco (1698). "Coinage of any of these mints had uniform currency throughout the entire Spanish Empire, and the pieces had uniformity of type." Each mint employed a variety of mint-marks. Gold was not minted uniformly until after c. 1650. Until then, the colonies used silver.