These answers are about as good as you can get for hardcore realism-we really don't know that much about a lot of pre-Columbian America due to a lack of written records.
Just speculating, we could see the Inca doing in the Andes what the Han did in China-using their political dominance to impose a single ethnic identity over a wide geographic area. I'm skeptical that they could conquer the southern Andes as they were-that would require projecting a lot of power over a very large and very, very dry desert.
The cultures in North America would be vastly different, as political confederations made in response to European colonization would never have occurred. Entire tribes wouldn't even exist without European contact-the Seminoles, who formed as a coherent group from scattered people of different tribes fleeing white colonization, and the Comanche, who only became a separate people from their ancestral tribe due to the introduction of the Horse.
For the more complex cultures of North America like the Mound Builders and the Pueblo, there is some speculation among archaeologists that they were in decline before colonization. If this is so, with enough time the complex societies would re-constitute themselves, just as Europe eventually recovered from the fall of the Roman Empire.
In a far-off future without colonization (though going this long without European contact is pure ASB, something like "The Americas are whisked away to a different planet in 1491), Native American cultures would develop very strong maritime cultures, as the lack of horses and other pack-animals outside of a small place in the Andes would mean that water-based trade would be the most efficient and effective way of moving goods.
