Chung Hwa Travel Service (Taiwan)
4/F, Lippo Centre, Lippo Tower 1 89 Queensway, Wan Chai, Hong Kong Island
Phone: 2525 8315
The fastest way to get there is by the high speed airport train to Hong Kong Island then a taxi to the Lippo Tower.
Many people have made a visa run in one day. Apply in the morning and come back with a visa that night. Other people have tried and had a lot of problems because of time constraints and the bureaucratic attitude of that office.
I also read a report about Chang Hwa Travel opening an office at the Hong Kong airport in April 2003. I have not been able to confirm that the office was opened or that they support visa services for non Chinese. I have looked for it but was never able to find it.