You can go to HK Polytechnic University. But, I heard they open a new eye centre for children in Kowloon. However, the check is a little bit expensive compared to the "Street Shop". But, worth it since some tests are done by Professor and Lecturers from the University
They have one in Wanchai (Hopewell Centre, early booking is required). Very detailed tests. My boy is 3 yrs old. Though it's a bit expensive, I still think it's necessary.
I think I has mixed up the centres. The Hopewell Centre is the new one. However, the centre in the Poly U still open for public. The telephone for booking is 2766 5225 or 27665224. My friend says the booking are very full and may need to wait.