In my area, there's a really well done book called Anóoshi lingít aaní ká or Russians in Tlingit America that provides the Native perspective for the battles of Sitka in 1802 and 1804. It's not a first contact story, but it's a well-done history of how the Tlingit defeated the Russians, then were defeated by the Russian counterattack a few years later.

Yes! I just finished reading Invading Guatemala: Spanish, Nahua, and Maya Accounts of the Conquest wars by Matthew Restall, Florine Gabriëlle Laurence Asselbergs. While the spanish accounts are longer and more prominent in the book the Maya and Nahua accounts are very interesting, notably the fact that the Nahua viewed themselves equal to the Spanish conquistadors. The book does a good job showing the diversity of the America's as well. Very interesting read I recommend to anyone.

There are a number of them. One of the most famous is "The Broken Spears: The Aztec Account of the Conquest of Mexico", by Miguel Leon-Portilla. It's still considered a must-read in the field of Latin American History.

At the risk of being obvious, I should point out that Native Americans are not all dead (meaning that indigenous-settler encounters are ongoing) and that there are many contemporary and recent indigenous authors whose work is well worth reading. Louise Erdrich, Sherman Alexie, and Leslie Marmon Silko are all excellent if you're interested in literature, and of course there are many others. There's been a wonderful explosion of work by indigenous scholars in the past few decades as well. Robert Warrior, Jennifer Denetdale, Joanne Barker, Ned Blackhawk, Phil Deloria, Jean O'Brien, Vine Deloria, Jodi Byrd, Kehalauni Kauanui, Noenoe Silva... the list really goes on and on.

There is, of course, the famous "Bury My Heart at Wounded Knee". It's written by a white American and isn't exactly the most historically sound thing ever written (to say the least), but it is primarily an attempt to portray the conflict between the United States and the tribes of the Plains in the mid-19th century from the point of view of the Native Americans, relying on Native accounts of the matter.

Just to lower the tone from the academic works cited by others to a piece of pop-history :p.