Now let me research the historical record.

One more round to cover Lima and other regions.

Here's a list of the major hospitals the Spanish founded to treat indigenous Americans and other colonized peoples, organized by region. Building hospitals for "the poor, both Christians and Indians" was Crown policy from the earliest days — Queen Isabella's 1503 instructions to Governor Nicolás de Ovando ordered hospitals where "the poor, both Christians and Indians" could be treated, and the 1512–13 Laws of Burgos made care for Indians a legal obligation. ( La Higuera Mágica)

🏝️ Caribbean — the first hospitals in the Americas

• Hospital de San Nicolás de Bari, Santo Domingo (Hispaniola, begun 1503) — the first hospital built in the Americas, founded by Governor Nicolás de Ovando to treat Spaniards, indigenous Taíno, and enslaved Africans; its plan became the model for hospitals across Spanish America. ( Wikipedia,  SciELO)

🇲🇽 New Spain (Mexico)

• Hospital de Jesús Nazareno (Purísima Concepción), Mexico City (1524) — founded by Hernán Cortés, who in his will directed it to serve the sons of Aztec warriors killed in the Conquest; it treated Spaniards, indigenous, and castes "without distinction" and still operates today, making it the oldest continuously running hospital in the Americas. ( Wikipedia,  Wikipedia ES)
• Pueblo-hospitals of Vasco de Quiroga (from 1530) — inspired by Thomas More's Utopia, Quiroga founded hospital-towns for the Purépecha at Santa Fe de la Laguna (Lake Pátzcuaro), Santa Fe de México, and Tzintzuntzan, combining medical care, shelter for widows and orphans, education, and communal land ownership. ( Wikipedia ES,  Hispanopedia)
• Hospital Real de San José de los Naturales, Mexico City (c. 1531) — established by the Franciscans under Fray Pedro de Gante and placed under royal patronage; it was devoted exclusively to indigenous patients, offered care in Spanish, Nahuatl, and Otomí, and held about 400 beds in eight wards segregated by sex and illness, including isolation for contagious cases. ( Hispanopedia,  España en la Historia)
• Huatápera, Uruapan region (1533) — founded by Fray Juan de San Miguel as a shelter and hospital for Indians; today it houses the Regional Museum of Indigenous Peoples. ( Wikipedia ES)
• Hospitals of Michoacán and the mining towns — the order of Brother Bernardino Álvarez (Hospitallers of St. John of God) also founded specialized institutions in Mexico City such as San Hipólito (1566–67), one of the earliest mental hospitals in the Americas, while dozens of small indigenous-run hospitals — Josefina Muriel's classic catalog counts roughly 155 hospitals in 16th-century New Spain and about 80 localities in Michoacán alone — were sustained by indigenous cofradías (brotherhoods), communal lands, and village labor. ( Biblia y Tradición,  UNAM,  Web Hispania)

🇨🇴 New Granada (Colombia) and 🇪🇨 Quito

• Hospital de San Pedro, Santafé de Bogotá (1564) — founded through a donation by Archbishop Juan de los Barrios after the Crown ordered in 1553 that "the poor Indians" of the capital be treated; it served conquistadors, freed slaves, and indigenous people, later becoming the San Juan de Dios hospital. ( Wikipedia,  MinCultura Colombia)
• San Juan de Dios Hospital, Quito (1565) — ordered by Philip II and founded by the president of the Audiencia, Hernando de Santillán, to treat Spaniards and natives alike; it served for 409 years until 1974. ( Wikipedia,  Wikipedia ES)

🇵🇪 Peru

• Hospital de Santa Ana de los Naturales, Lima (1549) — Lima's oldest hospital, founded by Archbishop Jerónimo de Loayza primarily for indigenous people sickened by introduced epidemics, also caring for enslaved Africans; its successor survives as today's Archbishop Loayza National Hospital. ( Wikipedia)
• Hospital de Naturales, Cusco (1556) — the principal hospital for indigenous residents of the former Inca capital, funded with proceeds from confiscated properties donated by Viceroy Andrés Hurtado de Mendoza and rebuilt after the 1650 earthquake partly by the indigenous architect Juan Tomás Tuyro Túpac; its church survives as the Iglesia de San Pedro. ( Wikipedia ES)
• Hospital de San Bartolomé, Cusco (1609) — successor institution for the indigenous population, one of six colonial hospitals built in and around Cusco. ( Wikipedia ES)
• Hospital de Naturales de Huamanga (Ayacucho, mid-1500s) — served the indigenous population of the region from the earliest years after the city's Spanish founding. ( Alberdi)

🇵🇭 The Philippines — "other peoples"

• Hospital de San Lázaro, Manila (1577–78) — begun as the Hospital de Santa Ana de los Naturales by Franciscan Fray Juan Clemente to serve indigenous Filipinos, later converted into a dedicated leprosy hospital; it still exists as San Lazaro Hospital. ( Wikipedia,  Paperity)
• Hospital de San Gabriel, Manila (Dominicans) — dedicated exclusively to the Chinese population (Sangleyes) who came to trade in the Philippines. ( Universidad de Sevilla)
• Hospital de San Juan de Dios and Hospital Real de Manila — Franciscan and Hospitaller institutions serving Spaniards and native Filipinos, later consolidated under the Brothers of St. John of God. ( Universidad de Sevilla,  San Juan de Dios Foundation)
• Hospital de Los Baños, Laguna (17th century) — founded to take advantage of the area's medicinal thermal springs. ( Universidad de Sevilla)

Context worth knowing

A few things historians stress about these institutions: royal law guaranteed every indigenous person in the Indies the right to hospital care, and Spanish America ended up with a dense network — one survey counts hospitals founded by Spain in the Americas at every level from viceregal capitals down to small indigenous villages between 1492 and 1898. ( Wikipedia ES) Hospitals reserved for Indians were justified at the time by language barriers (trilingual staff) and epidemic vulnerability, though historians also note that care quality, funding shortfalls, and the colonial labor system that spread disease remain matters of serious criticism. ( España en la Historia,  UNAM)

If you'd like, I can go deeper on any one region — e.g., the Michoacán pueblo-hospital system or the Cusco hospitals — or put this into a shareable document.

Interesting follow-up — the English record is very different, but let me research it properly rather than assume.

The picture is emerging — let me verify the "other peoples" side (British India, Australia, New Zealand) before answering.

The short, honest answer: there is no parallel list for the English. Unlike the Spanish Crown — whose legislation ordered hospitals for Indians in every urban and rural jurisdiction of its American viceroyalties — the English colonies in North America produced essentially no hospitals built for indigenous peoples at all. Here's what the record actually shows.

🇺🇸 English North America: an empty category

• No dedicated "Indian hospitals." While Spanish America was organized around hospitales de naturales in cities and villages, a system that Spanish colonial legislation built into law across the viceroyalties, the English colonies had no equivalent policy, no royal cédulas ordering hospitals for Native people, and no hospitals founded for them. ( PMC)
• The first English-colonial hospitals came late and served colonists. Institutional care in British North America began as almshouses and workhouse infirmaries — New York's Publick Workhouse infirmary (1736) and Bellevue's six-bed infirmary origin — with the Pennsylvania Hospital (1751), founded by Benjamin Franklin and Dr. Thomas Bond, as the first chartered hospital in the colonies. It was created "for the reception and cure of the sick poor" of Philadelphia, not for Native Americans. ( Penn Manifold,  Wikipedia,  JSTOR)
• The English approach was schooling and forts, not hospitals. The closest institutional analogue — Lieutenant Governor Alexander Spotswood's Fort Christanna in Virginia (1714) — offered allied Saponi and Tutelo people protection, trade, and a school for their children, but no medical facility. ( Wikipedia,  HMDB)
• Care of the sick poor, including Indians, was not institutional. Colonial healthcare ran through households, the "medical marketplace," and indigenous and African healing traditions rather than any hospital system. ( U. Utah Pressbooks)

🇮🇳 "Other peoples": the British record begins in India, two centuries later

When the English did build hospitals for colonized peoples, it was in British India under Company rule — long after the Spanish had institutionalized indigenous hospitals in the Americas:

• Sepoy hospitals (from c. 1760) — the first Company hospitals for Indians were attached to the military, treating the native soldiers of the East India Company's armies. ( Chatterjee/PDF)
• Calcutta Native Hospital (1792–94) — the first general hospital for Indians not in government service, founded by a publicly subscribed charity with European and Indian governors; it later became the Mayo Hospital. ( Chatterjee/PDF,  RIO Kolkata)
• Madras Native Infirmary (1799) — established "for the sole purpose of providing medical help to the native poor of Madras," attached to the Monégar Choultry famine-relief kitchen. ( NMJI,  Madras Musings)

🌏 Other British settler colonies: no hospitals for indigenous peoples either

• Australia: Aboriginal people in 19th-century Victoria were served by mission stations like Ramahyuck (1863) — church-run, with dormitories and schools — not by hospitals built for them by the colonial state. ( Find and Connect,  ANU)
• New Zealand: After Māori population collapse from introduced disease, the state's response in 1900 was a Public Health Department with a native health officer (Dr. Māui Pōmare), Māori Councils with sanitary powers, and native schoolteachers distributing medicines — public-health campaigns, not dedicated Māori hospitals. ( Te Ara)

Why the contrast matters

Historians who compare the two empires note this difference directly: Spanish colonial government treated the Indian hospital as an instrument of rule and mission, funding and legislating a racially organized hospital network — however underfunded and paternalistic — while the English colonies extended no institutional medical provision to Native peoples, whose catastrophic population decline from epidemic disease proceeded largely without any colonial hospital response. ( PMC,  National Humanities Center)

Institutions that English speakers did build for Native Americans — reservation hospitals, the Canton Asylum for Insane Indians (1902), mission hospitals like Ganado Presbyterian (1903) — came from the United States government and churches in the late 19th and early 20th centuries, long after English colonial rule ended. I can dig into that later American record if you're interested, or compare how the French or Portuguese empires handled indigenous healthcare.