2 flights both have layovers. Do i need visa to leave the airport during layover?

1st flight

Returning flight: 13 hr layover in Guangzhou
Bali - Guangzhou - New York

Question: I am US passport holder and my wife is a green card Japan passport holder. Do we need entry permit and are we allowed to leave the airport during our layover?

2nd Flight:

New York - Bejing - Manila
Question: We are both US passport holders, our layover is in Beijing for 13 hours, do we need entry permit and can we leave the airport?