Beijing is an obvious choice. The Forbidden City, Tianmen Square, Mao's body, The Great Wall, Summer Palace are all massive tour attractions, and for good reason. But don't forget the small things... Getting lost for hours in the Hutongs, people watching, and trying that questionable street food are also all part of the experience.
I don't know how long you will be there... Xian has the Terracotta soldiers, but if you're short on time, Beijing has something similar, they are just much smaller. Shanghai and Hong Kong are fun international cities... but they have far fewer cultural attractions. If you are looking for mountains, Guilin, Lijiang, and Zhangjiajie (my second hometown) are all gorgeous. Suzhou has been described as the Venice of China. As another RJer mentioned, in Chengdu you can hold a Panda... I could go on and on. It really depends on how long you stay and what you are interested in.
Watch this video to learn a little about Chinese culture before you go: http://www.tudou.com/programs/view/AZbvpZ847-A/
Hope this helps. Have an incredible journey, wherever you are, wherever you go