Going to Shanghai for one week

Hi!

I am an USA citizen. I live in Tokyo. I am planning to stop in Shanghai on my way home to America. My return will look like this:

Tokyo -> Taipei (stay in Taipei one week)
Taipei -> Shanghai (stay in Shanghai one week)
Shanghai -> Los Angeles

Can I apply for and receive the permit to stay in Shanghai at the Tokyo office? Because I will be traveling from Taiwan, is there anything special I need to do?

Thank you very much!