My company, Consuul printing and Design, targets local private schools in the greater San Diego and Orange County area. We have seen that contacting the public schools directly is a waste of time due to the chain of command. If you want to reach public institutions you actually have to go through the district. These sales can be no doubt larger, but we have seen that private schools, booster clubs, and Associated Students Councils in Orange County and San Diego are easier to reach, more susceptible to cross-selling, and have more capital and creative freedom to offer us.
Hope this helps you reach schools in your area,