If you are set on going to China, personally SE Asia is more interesting, with better food and beaches, the distances you need to travel to see everything you are planning are immense so try fewer days in Beijing, a boring government city, you'll see most things in three days there, the Wall, Forbidden City, Wangfujing, etc. three days in PVG is plenty with a day trip to Hangzhou for the lake and tea market or Suzhou instead, and three days in the south between Shenzeng/Guangzhou, then HK, much more interesting, especially walking around the entire island from above, don't wait in line for the tram up, take it down taxi up so you don't waste time, wander the mid levels, etc.