10 days, starting in kong kong - advice?

SO now that americans can travel for 10 days visa-free, I want to plan a trip in early/mid june. I would be starting in hong kong. I am more interested in nature and ancient history so I don't want to visit shanghai or chongqing. My plan is to see guilin, zhangjiajie, and lijiang (yunnan), spending about 3 days in each location. Thoughts? Any other recommendations? what is the best way to travel between these locations?

(I meant Hong Kong in the title)