Well -- Since you asked for input -- The majority of American Indians do not like to be referred to as a Native American - they prefer to be classified under their tribal name. They consider it to be offensive to be referred to as a Native American (their tribal identity is lost). They were made captive with the title American Indian, they fought under the title American Indian and have obtained their freedom under the title American Indian (Cherokee). This is what they refer to themselves as, if given a choice between Native American or American Indian.
This term became popular in the 1960s and 70s during the Civil Rights Movement. This was a label - that once again was placed on these people without their consent. Please don't forget we are not just the United States of America - we do have the Cherokee Nation within our borders.
Native American is anyone that is born in America -- so that could be - The United States of America, Canada, Mexico, South America orLatin America.
Native Americans are not restricted to the United States of America - Hence we are broken out into Canadian Indians and American Indians with Mexico being Mestizos.
If you don't want to use the term American Indian (prefered by American Indians), Canadian Indian or Mestizo, then consider using the term Original People of the United States, etc. or Indiginenous People of United States etc.
Then break it down into their specifc tribes. Our "American Indians" are a very proud people and they prefer to be classified under their tribe - Commanche, Apache, Cherokee etc.
As always - this is just a suggestion and not meant to offend anyone..