Im an American flying round trip into PVG from Korea. What about 72 hours transit visa?

I'm currently booked on an international trip to Korea from San Francisco California. I'm flying into Korea from San Francisco and then back to Korea to the United States. I would like to book a round trip into Shanghai PVG airport from Seoul Korea and visit Shanghai for 2 days. I would be staying at a friends house in Shanghai ( so not sure if that counts as a place to register my 72 hr free transit? Also I know Korea is one of the Asian countries that is allowed for the 72 hr transit but is it eligible if I'm an Anerican coming into Shanghai from Seoul Korea and then returning to Seoul from Shanghai? Please advise.