I am looking for a good book that gives you the entire run down of important events during each Chinese dynasty (Shang to Qing) as a gift for the white SO, but is having a lot of trouble doing so. Any recommendations?
There are few books that go that broadly, and for good reason: it is incredibly hard to compress all that time into a single volume. I mean, try doing that for the entire political history of literally anywhere else. Not gonna happen. Trouble is that people will generally specialise in one time period or another, often one particular dynasty and sometimes even a particular period within that dynasty, so will concentrate around that specialise area. There are a couple of options for portions of Chinese history, though:
Imperial China, 900-1800 by Frederick Mote will serve as a useful introduction to the period from the fall of the Tang in 907 to the beginning of the visible decline of the Qing with the death of the Qianlong Emperor in 1799.
The Search For Modern China by Jonathan Spence is a pretty popular introduction to the Late Imperial period through to the near present, beginning in the Late Ming around 1600.
Otherwise I am unaware of any good broad sweeps that include Tang or earlier dynasties.
I'd recommend The Open Empire. It only covers up to 1600 but it does a very good job of describing cultural and social changes in China and its relations with the outside world.