I am planning to fly into either Beijing or Shanghai. I want to go to BJ, SH, Guilin and HK.

It is suggested to go through this route: Beijing-Shanghai-Guilin- HK. Taking the train as your main transportation will help you save some money.
1. There are high speed trains at Beijing South Railway Station to Shanghai.
2. Taking a train from Shanghai to Guilin requires more than 10h. It may not be a very comfortable trip. It is recommended to catch a plane.
3. There is no direct train or flight from Guilin to HK. Take a bullet train to get to Guangzhou first, and then take direct train from Guangzhou East Railway Station to get to HK.