Flying into/out of Hong Kong can be cheap, as quite a few budget airlines operate from the city.
From Hong Kong Airport:
Airasia flies to Bangkok and Kuala Lumpur from Hong Kong.
HK to Bangkok: Starting from about HKD470 for a one-way flight, with tax included.
HK to Kuala Lumpur: Starting from about HKD560 for a one way flight, with tax included.
Cebu Pacific has one of the best connections to the Philippines with very low price. Other flights from Hong Kong go to Shanghai, Singapore, Bangkok and several places in the Philippines.
Hong Kong to Singapore: one way ticket costs about HKD 560 up. From Singapore, Jetstar serves a big network around the region.
Hong Kong Airlines
With Hong Kong Airlines, you can reach all major tourist cities in Mainland China, such as as Guilin, Kunming, Hangzhou, Shanghai, and Beijing. Destination outside China is also served, such as Hanoi, Vietnam or Okinawa, Japan.
Flights to China on Hong Kong Airlines are not particularly cheap. It is even cheaper to take flights from Shenzhen airport across the Hong Kong border. The best place to make a booking for flights from China is through elong.
From Macau Airport
If you have time you could also consider taking the ferry to Macau (about HKD150 one way) and take a budget flight from Macau Airport. Both Air Asia and Cebu Pacific operate from there as well and the price can be even lower.
For more about flying from Macau, view this post by me.
The good thing about budget airlines is, besides the obvious fact that they are on the cheap, the booking is based on a one-way price so if you travel around the region, it is a good choice indeed.