I am planning a trip that will involve a stop in Beijing.

I understand I can stay 72 hours without a visa. Am I able to go outside Beijing visa free. Obviously I have to visit the Great Wall, plus I would also like to go ti Xian via high-speed train. Also, I will be booking a primary flight that will go to Beijing but then get another flight to a second destination three days later and return two or three days before my departure date from Beijing. In other words, is a stopover for visa free status only accepted if it's a stopover with the same airline.