Answer:
Christopher Columbus's exploration of Hispaniola
Christopher Columbus is widely considered the first European to land in the Central and Southern Americas. His expedition to Hispaniola in 1492 opened the gateway for further European exploration of the area.
Hernando de Soto
Hernando de Soto was involved in what was the earliest explorations of the territories north of Mexico in what is now the United States of America. Landing in Tampa Bay in 1539, his party took a route that saw them go through Florida, Georgia, Alabama, Mississippi, and Arkansas till the party turned back in 1542 after Hernando de Soto fell ill and died of fever.
Francisco Vazquez de Coronado
Francisco Vazquez de Coronado led also led an expedition into territories that are now in the United States and he did so only a year after Hernando de Soto. Taking off from Mexico in 1540 in search of the rumoured Seven Cities of Gold, his route took him through current south-western United States till he reached modern day Kansas. The expedition also ended in 1542.
Juan de Oñate
Juan de Oñate is widely considered to be the Last Conquistador as his was one of the later expeditions by the Spanish. Between 1598 and 1604, Oñate undertook expeditions such as the New Mexico, Great Plains and Colorado expeditions. He is today remembered for the cruel retribution he meted out on the Acoma people that earned him a banishment from New Mexico.