Some general information about public schools in Hawaii can be found on the Department of Education schools page.
To search the DOE's member schools on the Big Island, click find my school.
For more information on independent private schools, go to the Hawaii Association of Independent Schools.
One of the most popular schools is Parker School in Waimea. I found the link on the web site above. You can search for all the schools on a given island or in a given city at the link above.