Hawaii Kai is home to a number of very good public schools. Elementary schools include Koko Head Elementary, Kamiloiki Elementary and Hahaione Elementary. The Middle School is Niu Valley and the High School is Kaiser. Hahaione, Niu Valley and Kaiser offer a full K-12 International Baccalaureate program. Nearby Aina Haina Elementary also feeds into Niu Valley Middle School.
Hawaii's schools have notoriously short summer breaks. For public schools, the school year ends at the end of May and reconvenes in the later part of July. Many parents ask what options are available. I've begun compiling an informal listing of programs and links which can be found here.
You'll also find access through the top menu as a subcategory under Education.