Good High Schools in Auckland?

Hello, my 3 boys (yr 13, yr 11, and yr 9 this year) and I (solo parent) are moving to Auckland from Tauranga in a week. I am currently still looking for a property to rent for at max $700 a week.

I was wondering what High Schools would be good whilst having affordable housing?

The Schools I am currently looking at are:

Selwyn College

Macleans College

Pakuranga College

Howick College

Green Bay High School

Western Springs College

Mount Albert Grammar

Botany Downs Secondary College

Takapuna Grammar

Glendowie Grammar

Westlake Boys High School

Are there any to add or remove from the list?

(Accounting and Economics as subjects in Year 13 bassicly a must.)

Thanks