US News rankings are biased heavily by average SAT scores and donations by alumni.
Public Schools are ranked lower because as a state institution they have larger goals than worrying about rankings (state mandates, improve surrounding community, bring education to the masses). Private schools do not have such constraints and can try to improve rankings by adjusting incoming SAT scores. I know of a private school that decided to improve their overall score by taking the highest of section score from any sitting and combining it instead of the highest overall. They've shot up into/near the top 25 over the past several years.
Also, since people who go to private school tend to be wealthier (in absence of scholarships), they can usually afford to donate more.
Thus, I don't think US News undergraduate rankings are really indicative of the best schools. Look at UC-Berkeley for example. It is ranked extremely high (top-10) in so many subject lists (i.e. Engineering, business) but isn't even top 20 overall.
Disclaimer: i am not affiliated with UC-Berkeley at all.