Shanghai will be humid and cool in mid Nov so you'd better prepare autumn clothes, such as long-johns and jacket. Beijing will be cool but dry with wind sometimes so that a little bit warm clothes should be prepared. Anyway, please pay attention to the weather forecast before leaving.

Both of Shanghai and Beijing are good places to do shopping and nice food. I think you could read this website's introduction on these two cities. As for historical places, obviously, Beijing is well-know. Ps: these historical sites of Beijing are very large, so please make sure that the elder are energetic.