The school used in the movies exterior shots was the same one used in Ferris Buellers Day off. The director John Hughes that also came up with the idea for the Breakfast Club thought the actors should eat lunch with the students in the school to try and stay in character. However Jud Nelson was said to get into character even off screen so much that he was almost fired. Below is a short video featuring both The Breakfast Club and Ferris Buellers Day off filming.
Here is what they all look like now