Visiting Shanghai but stopover in Bejing

Hello, I am coming from the US going to Shanghai then Osaka, Japan, but the plane is stopping in Beijing first before heading to Shanghai so my customs would be done in Beijing. I know I would be able to get the 72 hour free transit at the Beijing Airport because that is where my customs will be done, but my plan is to visit Shanghai, not Beijing. But from my understanding is where you get the permit is where you have to stay throughout the 72 hours, or would an exception be made since Beijing is just a short layover?