I know, not everybody likes the traditional schools and to be honest, you should be relief that in Jogja you can actually find, not just one but 2 Montessori schools.
I personally been to one only, which is Bambini Montessori school (More details below) and I didn’t really like it for my son, because unlike what I understand Montessori schools should be, this one was a bit too secluded, small class room with not enough natural light. But dont take my word for granted, I didn’t enter all class rooms and I didn’t check the other Montessori school.
Also another interesting comment is that the school is supposed to be fully english, but again, in my case I find out that actually half or less than half of the day was in english and the rest in plain bahasa Indonesia.
Bambini Montessori School
Jogjakarta Montessori School
Their website: https://www.bambini.sch.id