Where do I apply for my 144 free transit from the US - Shanghai - Beijing

I will depart from the US, arriving in Shanghai to catch another onward flight to Beijing. There will be a layover in Shanghai of 2 hours 15 minutes. So, I was wondering which airport (Shanghai or Beijing) will I be required to apply for the 144 hour free transit?
Also, after spending a few days in Beijing, I will depart Beijing to visit other Asian countries. However, upon completion of my Asian travels, I will return to Beijing to catch a flight to return to the US. Will I be eligible to obtain another 144 hour free transit while spending 2 days or so in Beijing before taking a flight back to the US?