If you're interested in the Amerindians (natives of both North and South America, sans Inuits and a few others) rather than strictly North America, then I'd recommend Charles C. Mann's "1491: New Revelations of the Americas Before Columbus".

It's popular history and a tertiary source, but unlike many such books, it's generally thought highly of in this subreddit. Search in this sub on "1491" and you'll see. I'm not an historian myself, and I found it a great overview. There's probably nothing new to historian's who specialize in this area, but it's a good introduction. According to the reviews here, there are only a few questionable claims.

Mann says that he wrote the book because much research in this area over the last few decades hasn't found its way into school curricula or popular history yet. For example, the fact that the landscape that the first Europeans found was often anything but natural, with many aspects of it purposely modified by the Indians. An example is that in Eastern North America the Indians frequently set fires that burned out the underbrush in the forest, because it increased the amount of their favorite game (e.g. deer). It also discusses the controversy over the population of the pre-Columbian Americas. I could name other things that were a surprise to me, but you get the point.

"Native American" encompasses more than 10,000 years of history on two landmasses stretching from pole to pole; you'd be better served by picking an area, and then focusing down on a specific time period in that area if you want decent information. The AskHistorians Book List has a few books on Pre-Columbian America north of Mexico and a more extensive list on parts further south.