I used to live in Bengbu, Harbin, and Beijing, and I've also stayed in Shanghai and also gone to see the Terracotta Warriors.
Beijing is an intense city, but at the very least for historical value visiting Tiananmen Square is worth it. But if you go to a shopping tourist district, I recommend being leery of any young women who try to befriend you and try to get you to take them out. The are con artists.
Shanghai is also an intense city, but visiting the river with the view of the city is fun and epic.
The other cities you mentioned I haven't spent time in.
If you have any questions I can help out with, let me know.