This topic fits with Toad's ships and other stuff I suppose.
North America had advanced societies, some didn't get off the ground, like the Mississipian culture. They overtilled the soil with corn, lacking the knowledge of crop rotation. The Anasazi/Pueblo peoples were very advanced, and traded with the Valley of Mexico, but they never advanced beyond a certain point. There was the Calusa in Florida, a city state which controled a small empire in the everglades and beyond. There were many kingdoms and such recorded by Lewis and Clark, wiped out by smallpox. There was one area that were innovators. As you know, necessity is the mother of invention. If there simply isn't a need, the advancement doesn't happen. Northwest Pacific were innovators. They were warlike and competed with each other for raids. War is a good way to provide that need, or general competition.
In Mexico you had that competition. Mexica Triple Allaince had many enemies, including the Tarascans which had destroyed bronze working and had a stable empire, the most serious threat to them, but one neither they nor the Tarascans could defeat totally, it was a cold war. Though the Tarascans managed to win territory over because Tenochtitlan(which was the dominant power in the Allaince) was so unpopular villages would join the Tarascans, who would then be trained and obligated to defend it. There was also the Zapotec, Mixtec and others. The region was a huge place of potencial at that point.
In Andes, the Incans were very advanced, they had natural borders to the north with the Muisca, and the Mapuche to the south, and the rain forest tribes to the east.
Why did someone in Asia not colonize? No need or desire. Its said that China(Tang dynasty) could definitely had reached the West Coast. In West Africa you had struggle to be the successful power between the kingdoms there, other than the slave trade(which the Berber peoples like the Moors were infamaos for), there was no inclining of sailing the atlantic. Its know the Vikings did reach northern north america, but they didn't stay long.
Europe had just the right mix of competition for advancement, culture, and technology that made it possible. I imagine if China had stayed fragmented into many Kingdoms like in Europe, and the idea of the Middle Kingdom became like the idea of Rome became in Europe, that same thing would happen.
Remember too. No draft animals(Llamas in the Andes being the exception) in the New World. Animals make a huge difference. Trade allows inventions to travel around as well, and faster travel=more trade.