General:
* Academic
* Educational
* Scholarly
* Intellectual
* Learned
* Literate
Focusing on a school or institution:
* School
* College
* University
* Educational institution
Focusing on the study of a subject:
* Scholarly
* Learned
* Erudite
* Intellectual
Informal:
* Bookish
* Brainy
* Studious
The best synonym for "scholastic" will depend on the specific meaning you want to convey.