The main gate is the gate near the Boys' Dorm. The second is on the school parking lot, this is most likely an entrance/exit for teachers' cars.
Russell Northrop can be found here between 7:00 p.m and 11:00 p.m.
The first and second gates are unlocked in Chapter 2. The third entrance/exit is behind the Girl's Dorm, near the second gate. It takes you nowhere in Chapter 3 and Chapter 4, but to Blue Skies in Chapter 5. The fourth entrance is somewhat hidden. It is on the Observatory Track, but is in a hidden tunnel at about the halfway mark from the Library. It leads to Blue Skies Industrial Area and Happy Volts Asylum.
The school gates are locked during Chapter 1 similar to Rockstar's restricted area mechanic in the Grand Theft Auto series, where in Bully, players are expected to explore the academy first and familiarize themselves to it.