tour of beijing an shangahi

I suggest you go Shanghai first, and spend 2 - 3 days there, then visit Beijing either by rail or by air, and stay in the capital city for 3 -4 days.
in Shanghai, you visit the Bund and the Huangpu River, Yuyuan Garden, Shanghai Museum, and Nanjing Road. in Beijing, you should not miss the Forbidden City, Geat Wall, Summer Palace, Temple of Heaven, Hutongs.