Basically, ко́мната works almost everything. Кабине́т is a type of ко́мната, and there's nothing particularly wrong with calling кабине́ты ко́мнатами.
Кабине́т is a room for work. Some people might have кабине́т at their homes. Rooms at work are also often called кабине́ты. However, IMHO кабине́т works better for rooms where there's one important person or few people. When there are a lot of people working in the same room, I'd use о́фис. (Although the distinction is not clear-cut.)
In hotel, it's но́мер or ко́мната.
At school, rooms for study are usually named класс 'classroom'. In the university, rooms are usually named аудито́рия 'lecture room'.
If the teacher has his own room assigned to him, then it would be кабине́т. Teachers at our university didn't have a room of their own. When they didn't have classes, they could spend time in their department's room. Both the department and department's room are called ка́федра (although ко́мната ка́федры also works for department's room).
If your boss has a room of his own, then it's definitely кабине́т. Кабине́т нача́льника is a very common collocation.
Could аудиториа also translate to "auditorium"? In the schools I went to here in Quebec, it's what we called lecture halls (large multi-layered rows of desks ever increasing in height built in a semi-circular fashion to face an individual in the center, seating 100 or many more, depending on the room - description to ensure we are indeed talking about the same thing).