Well, you can refer to this itinerary:
Beijing - Xian - Shanghai - Guilin - Yangshuo - Hong Kong

Maybe, time will be too pressing if you don't choose domestic flights of China. However, Beijing, Xian, Shanghai and Guilin are highly recommended.

Beijing is the capital of China. Of course, you should see it. Xian once was the very famous imperial capital. The Terracotta Warriors and Horses there is a must see. Shanghai, Oh, a huge city. It can be the most modern city in China mainland. And Guilin has very stunning natural scenery. The Li River there is so charming.