Looking for a public or private school in Taichung or Taipei

Hi Everyone,

I am planning to have my son studies in Taiwan next year (elementary school) and i am currently looking for a good public or private school in taipei or taichung. I would like my son to study in private school however the cost is way too high compare to the public school.

My budget is around 150K - 200K max per year (That would include everything except dorm).

I am totally new in taiwan and any recommendation or suggestion would be greatly appreciated.

Thank you.