schooling - Seattle ( redmond surrounding areas)

We are looking at a move to Seattle (Redmond) and have 2 of our 3 children whom we are trying to find information on schools for. Which are the good school zip codes and indeed which are good recommended schools - we are from the UK , however have been working in India for the last 3 years, one of our children is in 2nd grade in the American Embassy school, and one is in year 1 at the British International school. Which schools do most expats use for their children ? Are there any international schools ? Which are the good public schools?

Many thanks for any information that you may be able to provide...