I am not sure what service apartments are near CUHK ... ideally you can come right from the airport to a service apartment.
I know these are all in Southern Kowloon Peninsula and may suit your budget:
telephone 25151331 - Jordan Rd ... requires a 6 month minimum lease and I believe is furnished, I cannot recall the name but have given you the number.
Excellent Court
The Lodge
Sharma TST
New World Hotel / Service Apartments
The Pennacle Apartment
Harborview Horizon in Hung Hum
All of the above are a bus ride / MTR ride from CUHK by at least 30 minutes or more.
Also you will becoming in August when a slew of people are looking for apartments so this may work for you or against you.
With a budget of HK13000/month you should most definitely be able to get a nice modest flat unfurnished up towards Fo Tan, Tai Wai, Tai Po, Shatin and can have some cash left over to just go to IKEA or Price Rite and get some furniture for low value.
Some other alternatives is a flat share situation I would advise staying clear of a sublet.