It seems like Columbus only made it to Central and South America, and there was Vespucci and some Vikings who made it to Canada, but who was the first European to make it to the United States?
The first confirmed Europeans in the current US was Juan Ponce de Leon's expedition in 1513. After the Spanish began piecing together indigenous geographic knowledge, they realized there was a large "island" north of the Caribbean. In 1512, King Ferdinand contracted Ponce de Leon - then governor of Puerto Rico - to explore and colonize this land. On April 2, 1513, the expedition made landfall somewhere between modern St. Augustine and Melbourne Beach (the exact location is unknown). From there, the expedition sailed south around Florida, making various stops along the coast until they reached Charlotte Harbor on May 23. There they were repelled by the Calusa and headed back to the Caribbean.
Ponce de Leon returned to Spain to report his findings personally and his role as governor of Florida was formalized. Upon returning to the Caribbean again, however, he became entangled in a conflict with Caribs who attacked Spanish colonies in Puerto Rico.
Fortunately for Ponce de Leon, the Calusa continued to repel any attempt by other Spaniards to jump his claim to Florida. Unfortunately for him, the Calusa would do the same to him when he finally arrived with a colonizing expedition in 1521. Ponce de Leon was fatally wounded and the colonists retreated with him back to Cuba, where he died.