144 Hour Free Visa as a U.S. Citizen

Hello. I am a U.S. citizen with a U.S. passport. I will be visiting South Korea and then onto China before heading back to the U.S. I am wishing to travel to Beijing and Shanghai while in China. I will stay in each city for three days (3). Also, my plan is to take the high speed train in between the two cities. Can I apply for the 144 day free visa to do this? Do you have to have a confirmed flight out of China to visit? I am thinking about using a standby ticket for my return.