Princeton-Plainsboro Teaching Hospital is located in the fictionalized setting of Princeton, New Jersey, in House M.D.
The series uses Princeton-Plainsboro as the hospital's name and presents it as a teaching institution in New Jersey. The wording can cause confusion because “Plainsboro” is also part of the hospital name. The canonical town association used by the series and its reference material is Princeton, while the hospital itself is fictional.
The production filmed many exterior scenes at Princeton University in Princeton, New Jersey. That real-world location helped establish the academic atmosphere of the hospital, even though the institution seen in the story does not exist. Interior hospital scenes were created or filmed separately for production purposes.
Trenton and Edison are real New Jersey municipalities, but they are not the town identified with House's hospital. Plainsboro is likewise a real New Jersey township and appears in the fictional hospital's compound name, which is why it is a plausible distractor. The question asks for the setting, not the second half of the hospital's title.