For American Indian authors, you could start with any work by any of the following. (I've suggested titles that might match the idea of "a mainstream classic" - although that terminology's hard to work with in this case.)

Louise Erdrich - Love Medicine
LeAnne Howe - Shell Shaker
James Welch - Fools Crow
N. Scott Momaday - House Made of Dawn
Leslie Marmon Silko - Ceremony
Thomas King - Green Grass Running Water
Joseph Boyden - Through Black Spruce (although that's since 2000)
Sherman Alexie - Reservation Blues (Tonto and the Lone Ranger Fistfight in Heaven is somewhere between a set of short stories and a novel, since all the stories are interconnected)
Susan Power - The Grass Dancer
Linda Hogan - Mean Spirit