What should I do if I will stay at a friend's home instead of a hotel?

I'm a US citizen living in Japan. I want to visit my friend in Shanghai without applying for a visa, so I'm thinking of traveling Japan -> PVG Shanghai (arrive 12/23, depart 12/29) -> Taipei, Taiwan -> Japan. Are there potential problems if I don't have a hotel booked and will stay at my friend's (a Chinese citizen) home instead? Are there necessary documents I should prepare, such as a letter from my friend? I read an account online of someone who tried to register with the police and the poice asked for strange documents such as paystubs from the visitor's job in his home country.