Children attend schools in Los Altos or Palo Alto, depending on where in Los Altos Hills they live. You can visit the websites for the Palo Alto http://(www.pausd.edu
) or Los Altos districts to see the boundaries and learn more about specific programs.
Generally, Palo Alto's schools are considered to be slightly better than those in Los Altos, although both are excellent. A client of mine who is a professor at Stanford noted that the variation between student scores within the student body within a given school in either district is greater than the spread between the median between the two districts. In short, if your child is a good student, he or she will get a good education in either Palo Alto or Los Altos districts.
You will pay about a 5% premium for a property in Los Altos Hills that attends Palo Alto schools, especially Gunn High School which is the most highly ranked and is highly sought after. Additionally, the Gunn district takes in a desirable part of Los Altos Hills that is closer in on the east side of 280, where the homes have flatter more useable lots.
You actually ask a nuanced question, feel free to contact me if you would like to go into more detail.