The option to save your game is not available during a mission.
Jimmy's dorm room
On the desk in the far corner of Jimmy's dorm room, after you've completed the Welcome To Bullworth mission in Chapter 1.
On Miss Danvers' desk just inside the school office in the main building, after you've completed This Is Your School in Chapter 1.
On the west end of the football pitch, after completing the Jocks Challenge mission in Chapter 4.
Old Bullworth Vale
In the small clubhouse building beside the lighthouse near the carnival entrance, once you've completed Preps Challenge in Chapter 2.
Dragon's Wing comics
In the basement of the Dragon's Wing comic store in the center of Bullworth Town, after beating Fatty's high score in the Nerds Challenge mission in Chapter 3.
Complete the Greasers Challenge mission in Chapter 3 to unlock the greaser hangout at the east end of New Coventry.
On the western side of the Blue Skies Industrial Estate, near the tunnel leading to Happy Volts Asylum, after completing the Townies Challenge mission in Chapter 5.