Shengzhou, Hangzhou and Ningbo are all reasonably close to each other; accessible by bus or, if the company pays, have your hotel arrange a private car. It's still pretty cheap. I'd make Hangzhou my base for these three cities.
Qingdao is 2 provinces north of these first three cities, in the Shandong Province. You can catch a plane out of Shanghai or Hangzhou straight into Qindao.
Foshan and Zhongshan are in Guangdong Province, waaaay to the south. Catch a plane out of Qindao and take it to Guangzhou. Both of these cities are accessible from Guangzhou by taxi or bus. Your trip spreads you out quite a bit, but travel in China is cheap. You're hitting some nice places so enjoy.