Hi, It will be a little cold in mid Nov in Shanghai and Beijing, especially Beijing. You need to take some warm clothes. You can spend 5 days in Beijing and 5-6 days in Shanghai. There are many scenic spots both in the two cities. Also, you can do a good shopping in each cities.
You can take flight from Beijing to Shanghai which is the fastest way. Bullet train is also a good way to travel between the two cities.