I could give you some examples of resistance.

The last Maya kingdom to fall to the Spanish was the Itza Maya who had an island city by the name of Nojpeten in the Peten region of present-day Guatemala. The Itza fell to the Spanish in 1697 after inciting rebellions and organizing continued resistance against the Spanish. A Spaniard by the name of Martín de Ursúa y Arismendi made it is his mission to go out and conquer the Itza to relive the glory days of his conquistador ancestors and to gain wealth and fame for his actions. He convinced the Spanish crown to fund a royal highway going from Merida to Guatemala, but in reality the highway was a way to move troops closer to the Itza and to use any attacks on the highway as an excuse to put down Maya resistance.

Another example of continued resistance against the Spanish were the native groups in the present-day state of Nayarit. It can be argued that the beginning of Nayarit resistance began with the Mixton War of 1540. The Mixton War was a sort of retribution rebellion by native groups such as the Cora, Tepehuan, and Caxcan peoples in the area against Nuño de Guzmán's crimes and atrocities as well as a response to Coronado's expedition as he swept northward into the present day US Southwest. The Mixton War ended in 1542 with a Spanish victory, but many of the native groups that fought against the Spanish retreated into the rugged mountainous area of the Sierra Madres which make up much of Nayarit and Jalisco. Serious attempts at subduing the Nayarit region began in 1592, but because of the terrain and decentralized power structure of cooperating native groups in the region, the Spanish made no serious headway until 1719. In 1719, drought, epidemics, and famine had severely weakened the native peoples living in Nayarit. Baltasar de Zunigi, Marquis de Valero and the 36th Viceroy of Mexico, sent a large force to subdue the Coras and established the Presidio de San Francisco Javier de Valero in 1721. In 1721, the Cora chief Tonati had led a delegation that met with Zunigi and the Spaniards and said that the Cora would accept the rule of the Spanish Crown if the Cora rights to their lands would be respected and their native government would be respected. However, soon after the delegation had returned to Nayarit, Spanish forces seized Mesa del Nayar in February 1722 and, by 1723, Zunigi's force had completed the conquest of the Coras, who were rounded up and confined within eleven Jesuit-controlled villages. The Sierra thus became fully incorporated into the Spanish colonial Empire.

In general, indigenous people were quite effective at resisting European colonization. While large empires like those of the Aztec and Inca are known primarily for having been conquered incredibly quickly, many other native people resisted colonization for a long period of time. For instance, the "Indian Wars" in the USA didn't end until the 1920s and there were indigenous revolts in the Yucatan peninsula into the 19th century. The Seminoles of Florida call themselves the "unconquered peoples" because of their long-term resistance to conquest by the US government. You could even frame modern events like the Zapatista movement of Mexico starting in the early 1990s as indigenous resistance to "European" colonialism. In other words, European conquest of the Americas was hardly a quick or easy task and they found significant resistance just about everywhere they went.

As one example, in New Mexico, Spanish rule of the colony was continually challenged by the Pueblo people living under the Spanish. From the first years of the colony in the 1590s when Acoma Pueblo refused to pay tribute to the Spanish governor there were constant revolts and small rebellions of varying efficacy. The most effective was the Pueblo Revolt of 1680 when a Pueblo leader named Popay (along with other leaders) organized a mass uprising of all the Pueblos against the Spanish. They captured the colonial capital of Santa Fe and forced the Spanish to flee the colony for the safety of El Paso. The Spanish colonial government remained in exile for 12 years, attempting - and failing - to reconquer New Mexico in 1682 and finally reconquering the colony in 1692. There were many subsequent revolts, but never on the same scale or the same effect as the 1680 Revolt. If you are interested in more details I did a whole episode of the AskHistorians Podcast specifically on the 1680 Pueblo Revolt.