Orabi, Arizona, is a Hopi Native American village founded sometime before the year 1100 CE. It is one of the oldest continuously inhabited settlement in the United States. The Acoma Pueblo and Taos Pueblo are also some of the oldest continuously inhabited cities in the United States. Both were founded more than 1000 years ago by Tiwa speaking peoples. The Zuni Pueblo is another example of a Native American settlement, founded and still inhabited by Native Americans. Zuni is mostly inhabited by the Zuni people, and has a 2010 population of 6,302.

The prevalent trend is that the very little continuously inhabited Native American settlements today are mainly found in New Mexico, and the rest of the American southwest. Although areas like: Detroit, New York City, San Francisco, have always been inhabited by Native Americans, none of these cities retain their Native American aspect to them; neither in name, architecture, or culture. Most modern day cities in the United States today are built on what was previously Native American tribal land.

The Pueblo culture in Southwestern United States is very unique in the broader North American Native American culture. The various peoples in the southwest built these Pueblos out of material that could last a long time. The arid landscape molded these people into a urban population, out of necessity and lack of resources. Scarcity highly influenced the development of the Pueblo. Many Native Americans were not city builders, and any permanent settlements they founded were not cities in the way we think of a city today. Of course, there are plenty of exceptions, such as Cahokia in Illinois, and several mound building societies around that area. For the most part, the Native Americans of North America were not an urban peoples.

I hope this answered your question. A good book for this would by "The City: A World History" by Andrew Lees. In specific, chapter 1, 2 and 3, would help out.

And of course, the story is much different when you get south of the United States. There, the peoples living central Mexico were an incredibly urban and cosmopolitan peoples.