Be careful with the answers. All of 08536 and all of 08550 are in the Plainsboro/West Windsor Scool District BUT only a part of 08540 (Princeton zip code) is in West Windsor Township and only a part of 08512 (Cranbury zip code) is in Plainsboro Township.
Most of 08512 is in Cranbury Township and goes to Cranbury Elementary School and Princeton High School since Cranbury does NOT have a High School. Also part of 08512 is in East Windsor Township. Most of 08540 is in Princeton Township and parts of 08540 are in various townships other than Princeton such as Plainsboro, West Windsor, Lawrence Township, Hopewell Township, Frankin Township, Montgomery Township, and South Brunswick Township.
It is NOT the zip code that determines which school district your children can attend. Zip codes actually can be changed by the Federal Goevernment without regard to school districts. ONLY the actual location of the home in the school district which is determined ONLY by which township the home is located that counts ZIP Code does NOT count at all. Hope this helps