Lower standardized test score averages do not suggest that race/ethnicity is an advantage in admissions. It’s simply reflective of overall lower test scores in certain ethnic groups. Native Americans’ average SAT scores are about 150 points lower than white students’ test scores, so the lower SAT score average just may suggest appropriate percentile ranks within the Native American distribution. For example, a 650 is only in the 84th to 88th percentile of the SAT sections for white students; for Native American students, that’s the 92nd to 95th percentile (depending on which section we’re talking about). The lower standardized test score average for Native Americans at any given school is simply a microcosm of this larger systemic differences in the scores.
In other words one might argue that it’s an advantage that Native Americans, or black students or Latino students, can achieve lower scores on the SAT and still get in. The counterargument to that is that it’s not an advantage, since they overall/on average score lower anyway, so they probably have about the same chances score-wise of getting in as a white or Asian student with an SAT score several points higher - because it’s harder for them to get those scores.
Anyway, I’m going to take a different tack and say that there’s not necessarily one school that’s better or worse for Native American students than any other; it would depend on the individual needs of that Native American student. Some students like to go to a college where there are other members of their ethnic group, where there are multiple clubs reflecting their ethnic heritage, where there’s historical precedent for members of their group at the school. And others don’t care about those things at all and select schools on the basis of other factors. The school for you won’t necessarily be the school for you because you are Native American, but because you are Native and there are other characteristics about the place you like. (That much is probably clear in part from the fact that I think nearly every Ivy League school and some non-Ivies have been suggested as the ‘best’ on this thread.)