Formal:
* Auditorium (for larger spaces)
* Lecture hall (for large spaces with a single speaker)
* Study hall (for silent work)
* Seminar room (for smaller, discussion-based learning)
* Lab (for science or computer-based learning)
* Studio (for art or music)
* Learning space (a more general term)
Informal:
* Schoolroom
* Room
* Space
* Study
* Lesson room
More specific:
* Kindergarten
* Preschool
* Recitation room
* Conference room
The best alternative will depend on the specific context and the tone you want to convey.