Whatever you are looking for, the first place to go to is the Hong Kong ticketing website or the HK Ticketing. Here you can order/book your tickets for most of the shows going in Hong Kong whether it is a play, a concert, or an opera.
The other place to check out if you want to learn some performing arts is the Hong Kong Academy of Performing Arts where you will find everything about dance, drama music, theatre and opera in Hong Kong. For more info go here.
For rather small but good plays, you may want to go to Hong Kong Players:
Hong Kong has the first fulltime comedy club in Asia for stand-up comedy:
The opera Hong Kong is an internationally prominent one and you would find there all sorts of productions but of course what is more attractive and more specific to Hong Kong are Chinese Opera and in particular Cantonese Opera which are becoming rarer and rarer. Like all Chinese Operas, it involves music, singing, martial arts, acrobatics, and acting. Needless to say that the martial arts are quite different than the ones we can find in western operas!
The Cantonese Operas differ from the usual Chinese in the skills and methods used but you have to be an expert after a while to be able to tell the difference!
If you want to find out more about the shows at Opera Hong Kong, here is where to look: Opera Hong Kong
Rm 1907, 19/F, Pacific Plaza
410 Des Voeux Road West
Tel: 2234 0303
Fax: 2234 0505
The other opera you may want to check out is the Opera Society of Hong Kong: Opera Society of Hong Kong
There are numerous museums and alikes in Hong Kong so do not worry, you will not get bored!
The good idea is to get a Museum Weekly Pass for HK$30 for some museums (the biggest ones). With this card, you can visit these museums as much as you can for a week. Contact the Hong Kong Tourism Board for more info.
Here is a non-exhaustive list of some of the most popular museums in Hong Kong: