US --> Beijing --> tokyo

Your itinerary, under the condition that you have mentioned all your stops is definitely eligible for 144 hour visa free transit in Beijing area.

You will print out your flight tickets and your accommodation booking confirmation and have those printouts with you. Also, you will declare in US that you will travel to Tokyo via Beijing using 144 hour visa free transit. After a short inspection of your flight tickets, you will be allowed to board the plane.

Upon landing in Beijing, you will approach 144 hour visa free transit where you will fill out a blue form and shortly after you will be get a sticker in your passport (everything free of charge) and you will be allowed to exit the airport.

When you exit the airport, you are allowed to travel and stay within the area comprising of:

Beijing City
Tianjin City
Hebei province

Quite a large area and Great Wall of Badaling / Mutianyu is within this area, so you are allowed to travel and to stay there as you wish. Of course, you are allowed to travel even farther as you can explore on the map.