You might consider reasonably rented serviced apartments in Kowloon. I personally recommend Dash Suites, who is an expert in serviced apartments in Tsim Sha Tsui. I was a past tenant there, where I could find everything I need in the apartment & the team is helpful and friendly;)
If you haven't already, have a look at our Areas and Suburbs in Hong Kong page, which may give you some ideas for alternatives.
Also have a look at our Transport and Driving in Hong Kong page to get an idea of the public transport system.
Public transit in the city is generally good, and you may not have to live especially close to the school to be a convenient distance away.
Best wishes,
Xavier