Chengde, Datong, Shanhaiguan, Qufu. Perhaps Shijiazhuang (for Zhengding, Zhaozhou Qiao). All in a reasonable train or express bus ride of Beijing. If you include flying then most of Eastern China is opened up, and there are innumerable possibilities.
Have you thought of buying a guide book?
Some foreign editions can be found in the Foreign Languages Bookstore on Wangfujing, in the bookshop on the top floor of the Yansha/Lufthansa Centre, and possibly in the large bookshop next to the Oriental Plaza on Wangfujing, or the Beijing Books City in Xi Dan although I haven't looked there.
Peter N-H