V--make sure you have an onward ticket for a third country. You cannot fly US/PEK/US and use the 72 hr transit visa. You must transit to a third country.
"1. This regulation does not apply to passengers who travel on a single return flight (e.g., Hong Kong – Beijing - Hong Kong), which means the destination and place of departure can not be the same. They need to apply for a transit visa before their departure."

BTW if you do go and need a guide, Simon works in the city as well as trips to the wall. Our rate for gas, tolls, parking and time about 8 hours, was 600RMB (about $100) Including Forbidden City. Simon does explain before but does not accompany you. (I will post Simon's info in Specialty Travel later) You pay extra for official tourguides. Tickets and cable car and FC were about $30/pax (of course, you can walk; warning--it can be steep and long). CC ride starts at tower 14 and if you want to take the luge down, that's tower 6. Just buy OWs.

I do know that from central you can take a direct bus to Mutianyu section of the wall, and you can easily tour Beijing city with a good transit map and patience. We stayed at the Marriott City Wall and it was close to the train station and a main bus terminal. (hotel was gorjus, too!) It's very close to a fairly new mall with very good small food court and a nice supermarket. You can visit a park by the in-city wall adjacent to Marriott.

I just hope you can figure a way to do it!