Unfortunately, Mexico is a bit outside my wheelhouse, so I can't comment on Aztec mining.

On the other hand, Inca and Spanish mining in the Andes is something I do know a bit about (okay, maybe more than a bit). The center of Spanish mining in the Andes was the famed Cerro Rico, or "rich hill", at Potosi, Bolivia. Popular legend tells that the silver mining potential at Potosi was only discovered in 1545, when Diego Gualpa (or Guanca) climbed the mountain to visit a summit shrine - a common practice in the Andes. On his way back down, he's blown over by a forceful gust of wind, landing in a silver vein, thereafter kicking off the Potosi silver rush.

Is the story true though? It seems unlikely, given indigenous knowledge of metallurgy and the extensive development of mining infrastructure at nearby Porco (we'll get there), that the Cerro Rico should have gone unnoticed until 1545. There's some lake core evidence for metal processing at Potosi starting around 1100, but little archaeological evidence for anything prior to the Spanish colonial period. That might be because it was destroyed by later development, or it might be that the mountain's status as a sacred wak'a limited pre-Columbian exploitation of it's mineral resources. Either way, if you want to talk about intensive mineral extraction in the Andes prior to the Spanish invasion, you don't go to Potosi, you go to Porco.

Porco is located about 35km southwest of Potosi. Prior to the Inca period, it appears to have been very sparsely populated. Everything changed when the Inca empire expanded into the region in the first half of the 15th century. The Inka seem to have built quite a few structures de novo at Porco, including: workforce housing, general industrial spaces, storage facilities, and a number of wind powered Andean smelting structures known as huayrachinas, which used the ever present wind rather than bellows to power their fires. The archaeological remains indicate that while metal production and food preparation were common activities, the other activities you might associate with domestic space (weaving, stone tool production) were nearly absent. This seems to mark the site not as a place of full time occupation, but rather a place inhabited by state conscripted laborers, perhaps seasonally. The Inca practice of conscripting local populations into state industries as a form of "labor tax" - the mita - is well documented. While working at the site it would appear that their needs were in turn provided for by the state, given the lack of regional pottery styles and presence of classically Inca ones. This interpretation is also supported by the overall lack of Pre-Inca occupation at the site, and the fact that both food and fuel would've had to be brought in from more agriculturally or pastorally productive areas. These sites continued to be occupied into the early colonial period, and that population may have been more permanent, though Porco was quickly dwarfed in metal production following the "discovery" at Potosi.

The buildings weren't the only Inca construction that the Spanish co-opted however. In terms of infrastructure it's quite clear that the Incas expanded upon and formalized existing road networks in the regions they conquered, and it's equally clear that the Spanish did the same. Building a new road, especially in the highlands, takes a substantial amount of effort. In the early colonial period (1532-1700ish), transport was mostly still done by herds of camelids along the same routes that had been used for hundreds if not thousands of years. In some cases, it appears that formal Inca roadside sites (known as Tambos) continued to be occupied into the colonial period. At the same time, in keeping with a longer history of Andean pastoral tradition, we find lots of ephemeral campsites along roads. Roads, tambos, and campsites continue to get used in the later colonial and early Republican periods, but transport regimes also shift in some ways in response to a growing reliance on mules over camelids. This is what my current research is focused on, so I don't want to delve into the deep nerd-dom and get too far away from mining, but I'd be happy to answer follow up questions.

Finally, while it isn't directly related to your question, it's important to note that the biggest thing the Spanish took from the Inca in regards to mining was the idea of the mita labor tax. Spanish administrators conscripted thousands of indigenous Andeans into deadly mining work at Potosi and the mercury mining town of Huancavelica every year - not only in the mines themselves, but also in processing facilities that routinely exposed laborers to dangerous levels of mercury. Very quickly, the Spanish realized that the local population could not sustain the demand for forced labor, and they drastically expanded the spatial extent of the Potosi and Huancavelica mita. Many mitayos (that is, able bodied men) walked for weeks. They were often accompanied from their home community by wives and children. Many did not make it home again.

Sources:

On Potosi:

Lane, K. (2019). Potosí: the silver city that changed the world (Vol. 27). Univ of California Press.

Bakewell, P. J. (Peter John). Miners of the Red Mountain : Indian Labor in Potosí, 1545-1650. 1st ed. Albuquerque: University of New Mexico Press, 1984.

On Porco:

Van Buren, M. (2021). The Persistence of Indigenous Silver Production in Porco, Bolivia. International Journal of Historical Archaeology, 25(1), 45-64.

Van Buren, M., & Presta, A. M. (2010). The organization of Inka silver production in Porco, Bolivia. Distant Provinces in the Inka Empire: Toward a deeper understanding of Inka imperialism, 173-192.

Van Buren, M., & Weaver, B. J. (2012). Contours of labor and history: a diachronic perspective on Andean mineral production and the making of landscapes in Porco, Bolivia. Historical Archaeology, 46(3), 79-101.

Van Buren, M., & Cohen, C. R. (2010). Technological changes in silver production after the Spanish conquest in Porco, Bolivia. Boletín del Museo Chileno de Arte Precolombino, 15(2), 29-46.

On Roads:

Corcoran-Tadd, N., Ulloa Hung, J., Antczak, A., Herrera Malatesta, E., & Hofman, C. (2021). Indigenous Routes and Resource Materialities in the Early Spanish Colonial World: Comparative Archaeological Approaches. Latin American Antiquity, 32(3), 468-485. doi:10.1017/laq.2021.6

Corcoran-Tadd, Noa, and Guido Pezzarossi

2018 Between the South Sea and the mountainous ridges: biopolitical assemblages in the Spanish

colonial Americas. Post-medieval archaeology 52(1):84–101. DOI:10.1080/00794236.2018.1461326.

Nielsen, Axel

2000 Andean Caravans: An Ethnoarchaeology. Unpublished PhD. Disseration, University of Arizona.

2016 Home-making among South Andean pastoralists. The archaeology of Andean pastoralism:231–

Garrido, Francisco

2016 Rethinking imperial infrastructure: A bottom-up perspective on the Inca Road. Journal of

anthropological archaeology 43:94–109. DOI:10.1016/j.jaa.2016.06.001.

Glave Testino, Luis Miguel.

1989 Trajinantes: caminos indígenas en la sociedad colonial, siglos XVI/XVII. 1. ed. Serie Tiempo de

historia ; 6. Instituto de Apoyo Agrario, Lima, Perú.

Yes, many new Spanish cities where built on top of preexisting native settlements, where they sometimes used part of the building. The city of Cusco is full of these, you can find many colonial constructions using the stone walls of ancient Inca constructions as base. For example the Coricancha(great god sun temple) is now under a colonial church

But if you mean completely repurposing a building, probably in the first days of the conquest since they didn't have other places to be. For example it's known that Pizarro kicked out chief Tahulichisco from his palace, and years later demolished it to built his house