We are generally taught about when Cortez and his allies in Tlaxcala defeated the Triple Alliance (Aztec) in 1521 and Francisco Pizarro in Peru in 1533. I also know Francisco de Montejo established Merida in the Maya region in 1542. But just because you conquer a capital doesn't mean you have administrative control over the whole territory. For example, I recently read on Wikipedia that Nojpetén was the last autonomous Maya settlement when it was finally defeated 176 years later in 1697.
So what other regions that were claimed by the Spanish Empire in the Americas were finally conquered and forced under administrative control of the Spanish after 1542?
Note: Thank you to the commenters for help focusing this question. I've now re-written to make it more specific.