Does it have to be in the Seattle city limits?
The school that closest matches what you are describing, in my opinion, would be the International Baccalaureate Program at Interlake High School in the Bellevue School District.
District website:
http://www.bsd405.org/Default.aspx?tabid=101
School website:
http://www.bsd405.org/Default.aspx?tabid=120
IB Program website: http://www.ibbellevue.org/ibinterlake.htm (broken link)
I don't think you'll find another public school program with higher academic standards or superior reputation.
In Seattle, Garfield High School is the magnet school for the district AP program.
And depending on where you live in the city, you may have access to the John Stanford International School:
http://www.jsisweb.com/jsis/index.asp
But is a highly sought after program with long waiting lists.