Where did Aeneas go to?
According to the Iliad Aeneas sailed away to the west – before impact – which means toward the Americas. There is not a lot of further evidence, but enough to speculate that he ended up in Mesoamerica – the region of southern Mexico / Guatemala.
Mesoamerica is recognised as another one of those centres, like Mesopotamia, where aspects of civilisation suddenly appeared – from unknown sources. According to orthodox accounts, the pre-Olmec and pre-Mayan civilisations spontaneously emerged, at least as early as 8000 BC.
There is not a lot of direct information for a number of reasons. It was a very long time ago; maybe there were never many records; those that do survive have resisted translation; and most tellingly, the little surviving written records were actively destroyed by the Spanish conquest. When Conquistador Hernan Cortes defeated Montezuma in 1521 his Soldiers of Christ set out to kill the ‘Sons of the Sun’ and destroy their culture. While the soldiers looted the heathen temples for gold and jewels, Bishop Diego de Landa collected a large number of books made of tree-bark and he burned them all – explaining, ‘they contained nothing but superstition and lies of the devil, [so] we burned them all, which they [the Maya] regretted to an amazing degree and it caused them much affliction.’  They cried tears for the loss of a slice of human history.
Bishop De Landa goes down on the list of world-class villains, for burning our history.
There is not much direct evidence, but a long list of coincidences.
The pre-Olmec/ pre-Mayan civilisation emerged spontaneously, from unknown sources.
The so-called Tikal frieze, from a stone temple at Tikal, shows a scene of a man in a boat rowing away from a landscape of volcanic eruption and a stone pyramid crumbling as if by an earthquake – open to interpretation as the pre-Olmecs fleeing from violent destruction of their homeland. Unfortunately, this frieze was sent to the Berlin museum and was later destroyed by bombing in WW II, leaving the surviving records open to doubt.
Written records of the Popul Vuh of the Maya, surviving in documents known as the Dresden Codex and the Chillam Balam, also claim their motherland was destroyed in violent upheavals and fire and was swallowed by the sea. The day became as night and survivors went underground.
The Olmec arrival in Mexico coincided with the emergence of written language and numbers, knowledge of astronomy, stone construction, and cultivation of crops notably including maize.
According to modern analyses, domesticated maize (corn) originated – as an oddly singular event – in this same region in about 7000 BC. 
Stone construction included the erection of large stepped- pyramids, obviously similar to those of ancient Egypt.
Again parallel to ancient Egypt, the Olmecs / Mayans called themselves ‘Sons of the Sun’ and also used a year of 360 days, plus an ‘added’ 5 days. The period of the added 5 days – the wayeb – was associated with a time of great danger or disaster.
The stonework was Cyclopean in scale and sophisticated in execution with very fine, mortar-less joints. The ruined pyramid site of La Venta included a wall of ‘basalt prisms’ weighing tens of tonnes each at a location tens of kilometres across dense jungle from the nearest possible source. How that was accomplished remains obscure. ‘Basalt prisms’ are large regular columns with a polygonal cross-section, known to appear naturally as molten basalt (lava) cools. However, there are few known occurrences in the world and only rare instances where they have been used in construction – including here in Mexico and the even more remote Pacific island of Pohnpei – both oddly associated with the children of Aeneas.
The earliest Olmec records include a variety of objects and materials that were not indigenous – indicating that the people were not insular but must have had the ability to travel and trade widely.
Later regional legends included a widespread and strong belief in a ‘white lord’ called Viracocha, of bearded European appearance. He arrived by boat with a few companions, then after an indeterminate period, they left equally suddenly, never to return. Viracocha was said to be Lord of the ‘dark world’ without sun, ‘from the beginning’; but also to be the ‘bringer of light’ from the sun, moon and stars – which is all oddly reminiscent of Genesis.
Regional creation myths also said the pre-Olmecs were the Tamoanchan who re-peopled the world after the gods destroyed the [prior] human race in the ‘underworld’ of Mictian, to the north. Then one day Viracocha packed up his people and sailed away, westward to Mesopotamia.
Of course, none of that is conclusive but it is rather a lot of coincidence.
What did Aeneas do in Mesoamerica, and why did he leave for Mesopotamia?
Answers lie in legends on both sides of the world.
After Aeneas fled the destruction of his homeland he faced a new world dominated by water and darkness. Ice melted, sea levels rose, and dust, smoke and volcanic ash clouded the skies. Hebrew scripture recorded simply – In the beginning [of the new world] darkness covered the deep. (Gen 1). It was particularly bad in the northern hemisphere because atmospheric pollution tends to stay mainly on its own side of the equator. It was a massive, persistent, hemispheric effect.
In western Europe vivid ‘Stone Age’ art flourished in the wall paintings of the caves of the Dordogne up until about 10,000 BC then suddenly stopped, and recognizable human activity did not re-emerge until the ‘megalith builders’ about 4500-4000 BC. Similarly in ancient Egypt Stone Age flint quarries and hunting camps flourished from 100,000 BC onward – but from around 11,000 to 8,000 BC there is no evidence at all of human activity in the Nile valley. Likewise in Mesopotamia, modern scientific reviews of radio-carbon C14 dating of archaeological sites reveals a puzzling ‘gap’ between 10,000 BC and 8,000 BC – where there are no dated records.  At Mycenae in Greece, late Neolithic cave dwellers exhibited progressive activity and sophistication up until about 10,000 BC, but then until about 7,500 BC the population actually declined and excavations show they subsisted mainly on fish.
It was a world of dark despair. The Mesoamerican records say day became as night and the survivors went underground. In Europe men became troglodytes … mortal men sought shelter from the inclemency of heaven and were driven into caves.  Lower, rude races were simply thought ‘to have come out of a hole in the ground’. Even the noble Greeks came from ancestors who were savages, beasts dwelling in mountain caves, and clefts unvisited by the sun – later grandly called autochthonous, meaning ‘earth born’. 
Against that context, there are three sets of parallel legends.
Mesoamerican legend records Aeneas (or his son/s) as the lord of the dark world from the beginning, but then as the ‘light bringer’ who made the sun and the moon and the stars. Until the day he abruptly packed up and left, by boat across the ocean.
On the other side of the world in the Middle East, Hebrew [religious] scripture likewise witnessed that ‘God’ [first] created Earth with darkness on the face of the deep, then [later] He made the two great lights to rule the day and the night, and the stars also … and a mist went up and all was good (Gen 1). In Josephus’ version (in Greek) ‘God’ (Elohim, plural) created heaven and Earth but Earth was covered with thick darkness.
And in western Europe, secular pagan folklore captured the same collective memory in the tale now known as Sleeping Beauty. In the Golden Age, there was a christening party (where the baby was doused with water), but a dragon chariot (from the sky) delivered a metal spindle which wounded the Princess and cast everyone in the whole kingdom into a deep sleep. Within minutes the whole kingdom was cast under the gloomy cover of trees and brambles so almost nothing could be seen, and the dark forest was inhabited by witches and ogres. Then after hundreds of years the son of a king from a different family on the other side of the country arrived and fearlessly explored the dark forest – finding a horrible scene of death everywhere with men and animals lying dead in drunken disorder. He entered the old castle, found Sleeping Beauty and opened the bed-chamber curtains – at which the Princess awakened into bright, golden resplendent light. She was kissed by the sun, the Prince of Light. The Prince and Princess were married and had two new children; curiously called ‘Morning’ and ‘Day’, and all the people were restored to life in daylight. 
In Grimms familiar English version (published 1812) the children were called Morning and Day after Perrault’s earlier French rendition (Aurore and Jour) – which incidentally was published in 1697 as Histoires ou contes du temps passé … not ‘fairy tales’, but histories of past times. But in Basile’s even earlier version (published in 1528 from sources known around 1340), the children were twins named ‘Sun’ and ‘Moon’.
In other words, the young ‘Prince’, son of the King from far away, made the sun and the moon, bringing light.
The surviving ‘lords’ of Aeneas’ noble race sent their son/s to Mesopotamia to save mankind from the darkness.
 De Landa’s Relacionde las Cosas de Yucatan, Peabody Mus, 1941
 Matsuoka, 2003. Earliest Directional Evolution for Microsatellite Size in Maize. Science.
 Spencer,1993. Early Egypt. The Rise of Civilisation in the Nile Valley
 Hole, 1987. Issues in Near Eastern Chronology, Brit Archaeological Report S379
 Ovid, Metamorphoses, The Silver Age.
 Aristotle, Politics, in Lang, A. Myth, Ritual & Religion
 Grimm Bros, Sleeping Beauty