The tooltips for "食堂" should be updated to include the term "cafeteria". As an American English speaker, I've never heard the term "canteen" used for anything other than a traveler's container for alcohol or water.
We definitely call the school restaurant the cafeteria. Cafeteria is the only word that I have ever used to describe the eating place in an American school. Canteen or cantina definitely sounds like a place where you would enjoy adult beverages. :-)