If your looking for western boxing then I suggest DEF boxing gym in Sheung Wan. All the rest of the gyms that provide boxing are just kickboxing instructors teaching how to punch. Its not boxing. Having boxed for a while I thought DEF is great especially for beginners. The problem is if you want to fight and train like a fighter, then you may find it hard to progress unless your willing to pay for private tuition with a coach. If you prefer Thai Boxing then I used to train at Arena Thai gym in Wan Chai. The place was my second home and the owner Bryan is a great guy. Samkor a legendary Thai fighter is the main instructor and classes run all the time. The one thing I would warn you about is that it is more of a local gym. You don't see many expats. Another suggestion is impakt in central, loads of expats train there