I can answer on the Central American countries and maybe give a bit of insight more broadly.

When the Spanish colonised the Americas, they split their colonies into vast subdivisions, like New Spain (almost all of their North American possessions) and New Granada (the northern third of South America). These were not independent states, nor were they ruled directly from Madrid, but were rather governed by a viceroy, or a governor empowered to act in the name of the king. What we would think of as their "capital cities" would typically be the location of the Audiencias Reales, or royal courts, from which Spain could project its power and authority via these viceroys. Spain had no way to predict that their empire would collapse, and that their vast viceroyalties would split into various smaller states, so the construction of cities like Tegucigalpa or Managua was completely unrelated to the need for a "capital city".

So how did inland Spanish colonial cities grow to be so big? Throughout the colonial period, the areas under Spanish control were actually relatively small. Cities could be fortified and strategically located to project power and pacify resistance, whether from natives, slaves, or dissatisfied mestizos. Inland cities, like Tegucigalpa, were also frequently located near natural resources like gold or arable farmland. Furthermore, inland cities like Mexico City would profit hugely off their central location via trade, as they were often situated on the crossroads between the Atlantic and Pacific Oceans, as well as drawing in locally-produced goods from the surrounding areas.

u/PearlClaw also mentions below that climate is an important factor. I can add the example of the Salvadoran coast, where the average daily temperature is 34°C, compared to the somewhat cooler higher elevations of San Salvador. Founding cities at higher elevations was common across many imperial powers, one example being British plantations in India.

Now, why did the newly-independent countries established in the early 19th Century set their capitals in inland cities? In the case of Central America, there was often no clear centre of power (Guatemala City aside, which served as the capital of the United Provinces of Central America). The region was still seen as a frontier/backwater at the time of independence. For instance, in the 1830s Guatemala City had a garrison of just 250 men, with fewer than 600 soldiers in the rest of the country. Local caudillos (strongmen) effectively reigned as feudal lords, and any central authority was minimal.

The 19th Century for much of Latin America was defined by the conflicts between Conservatives (i.e. the old aristocracy and landholding elite) and Liberals (i.e. wealthy merchants and capitalists). The push and pull between these groups would define where the capital was located, and indeed it would move very often. Honduras rotated its capital between the Conservative Comayagua and the Liberal Tegucigalpa until the 1880s. Nicaragua set Managua as a capital as a compromise between Liberal León and Conservative Granada.

In short, there's no one answer to why these capitals are located where they are today, but the many contributing factors speak to the complex history that defines the region.

Sources:

James Dunkerley, Power in the Isthmus

Miles L. Wortman, Government and Society in Central America, 1680-1840

I can only speak to Guatemala, and I hope that this specific case can help shed light on your question. I will first examine the broader history of Guatemala’s capital cities, and then elaborate on several factors that were significant in selecting these sites.

The Three Santiagos

The modern Guatemala City was actually not the capital of Guatemala for most of the colonial epoch. The original capital was established by the conquistador Pedro de Alvarado in 1524. After invading Guatemala from Mexico, he allied with the local Cakchiquels against the Kiche and Tzutujil polities and won several major battles (Hill p.20). He returned to the Cakchiquel capital of Ixmiché and declared it to be his own capital, renaming it Santiago (Herrera p.6). He then rewarded his Cakcuiquelallies by demanding tribute and forced labor. That same year the Cakchiquels abandoned Santiago and waged a rebellion, led by two leaders Belehe Qat and Cahi Imox (Hill p. 21).

In 1527, Alvarado and the Cabildo of Santiago decided to reclocate to a slightly different location at Almolonga, where they founded Santiago #2. Unlike Santiago #1, Santiago #2 was more defensible due to the volcanoes and had a better water supply. Ironically, in 1541 Santiago #2 was largely destroyed by a mudslide off the slopes of the Agua volcano. This killed 600 Indian slaves and 100 Spanish settlers in a city that had at most 150 Spanish households (Lutz p. 7). Bishop Marroquín of Santiago wrote “that by necessity we moved it, since [the tragedy] was caused by water and it well could be that [other such floods] will come,” (Lutz p. 7).

In 1541 the vecinos voted to move the city. Bishop Marroquín and Francisco de la Cueva (Alvarado’s brother-in-law) selected a site in the Panchoy Valley and found Santiago #3. Possible reasons include the defensibility provide by nearby volcanoes, water supply, and large Indian population in the already established milpas and farms of the region. Santiago #3 would remain the capital until 1775, when it was heavily damaged by an earthquake and Guatemala City was designated the new capital. Santiago #3 is currently known as “Antigua Guatemala”.

Local Decisions

Something that should be clear with these choices is that the three Santiagos were NOT centrally-planned from Spain. In all three cases, it was local leaders and Spanish colonists who decided where to set up shop. In the case of Santiago #3 there was even an opem discussion, although Bishop Marroquín and Francisco de la Cueva selected a site different from the original majority preference (Lutz p. 8).

In addition, these choices also had indigenous precedents. Santiago #1 was directly founded on the Cakchiquel capital Ixmiché. Santiago #2 was built on the site of a pre-Hispanic Cakchiquel settlement (Lutz p.6), and Santiago #3 was just north of Santiago #2.

Control of Indians

Something that should be apparent is that the fundamental security issue for the Spanish colony was the control of Indians. All three Santiagos were founded with military security in mind, especially in the wake of ongoing warfare with various Maya polities. The Spanish regarded the landlocked, high-altitude city surrounded by mountains as a secure site to defend precisely because of its relative inaccessibility. In some regards, the Spanish colonial settlements functioned more like islands of sovereignty connected by corridors of roads than as the homogenous imperial blobs portrayed on maps (Benton).

Agriculture and Trade

Unlike Mexico and Peru, agriculture was the primary economic attraction of colonial Guatemala (Herrera p. 9). Disappointed by the lack of precious metals (which is one of the reasons why Alvarado demanded tribute from the Cakchiquel), Guatemala’s chief exports were cacao, indigo, and foodstuffs like maize and wheat, along with indigenous textiles (Herrera p.33). All of these ultimately relied on the exploitation of indigenous labor, making the Valley of Guatemala an attractive site due to the large indigenous populations.

Santiago de Guatemala quickly developed into a major commercial center with connections to major Mexican cities (above all Mexico City) and to the peripheral cities of Central America (Herrera p. 30). Transportation was an issue. However, this was handled Indian carriers for some short distances (Lutz p. 148), with teams of muleteers for general purpose and especially overland freight (Herrera p. 59), and Puerto Caballos (modern Puerto Cortés in Honduras) for direct contact with Spain (Herrera p. 24).

References

Benton, Lauren. A Search for Sovereignty: Law and Geography in European Empires, 1400-1900. Cambridge University Press, 2011.

Herrera, Robinson A. Natives, Europeans, and Africans in Sixteenth-Century Santiago De Guatemala. University of Texas Press, 2003.

Hill, Robert M. Colonial Cakchiquels: Highland Maya Adaptions to Spanish Rule, 1600-1700. Harcourt Brace Jovanovich, 1992.

Lutz, Christopher H. Santiago De Guatemala, 1541-1773: City, Caste, and the Colonial Experience. University of Oklahoma Press, 1997.