I noticed that over at /r/AskAnthropology you've already been given 1491. I recently finished reading that one myself. It's an interesting book, but be aware that it's mostly a history of academic positions on Pre-Columbian history than it is a Pre-Columbian history itself. Every now and then, you'll get some extended sequence of Pre-Columbian history in there though.

For more detailed histories, here's a quick list of suggestions that should provide a good introduction to their relevant topics. Some of these also discuss post-Contact history as well.

North America

• Ancient North America
• The Moundbuilders
• Ancient Peoples of the American Southwest
• The Iroquois*
• The Timucua
• Cahokia (Pauketat has several books on Cahokia; I picked this one because its the most reader friendly of the bunch. If you're looking for something meatier, check out his other works).
• The Cheyenne
• The Ancient People of the Arctic
• The Northern World: AD 900 - 1400

Mesoamerica

• Mexico: From the Olmecs to the Aztecs
• The Olmecs
• The Maya
• The Ancient Maya
• The Aztecs
• The Aztecs

South America

• The Incas
• The Incas
• The Tiwanaku: Portrait of an Andean Civilization
• Tiwanaku: Ancestors of the Inca
• The Moche
• The Nasca

Also, if a local library has them or if you feel like spending a lot of money, you might also be interested in the The Cambridge History of the Native Peoples of the Americas. Volume 1 covers North America, Volume 2 covers Mesoamerica, and Volume 3 covers South America. Each volume is divided into two parts. It'll help cover the sizable gaps in this list.

*I always forget to add these footnotes. Anyhow, I was going to mention that in "The Iroquois" Snow favors a late date for the formation of the League. Fagan in "Ancient North America" does as well, though he doesn't commit to a specific year. Late dates, 1450-1560 CE, straddle the transition from Pre-Columbian to Post-Columbian, but pre-date direct European contact with the Iroquois. However, another faction of historians and archaeologist favor an early date, 1142 CE, as initially proposed (academically at least) here. All these dates are based, in part, on oral history and an associated solar eclipse. Snow favors a late date due to the combination of archaeological signs of violence (the League forms as a response to internecine warfare) and a late eclipse in the region; Mann favors an earlier date because the eclipse at that time aligns best with Seneca territory (later eclipses would only be partial eclipses in this important region), the archaeological evidence that maize became a dominant crop at this time (an often overlooked part of the oral history concerning the League's formation), and a combination of other factors, such as the number speakers the League had before contact and genealogical information preserved orally.