Which cities in China are self-governing cities? Beijing, Shanghai, Changsha, Shenzhen

The self-governing cities of the People's Republic of China are provincial-level administrative units. They are not provinces, but have the same rank as provinces and autonomous regions and report directly to the central government of the People's Republic of China.

There are four self-government cities in China. These are:

Beijing , the capital of China;
Tianjin , a port city 120 km south-east of Beijing;
Chongqing , by far the largest in terms of area - and thus also the largest in terms of population - of the four cities whose administrative area used to form the eastern seventh of Sichuan Province ;
Shanghai , the economic and financial metropolis at the mouth of the Yangtze River .

So only Beijing and Shanghai are the self-governing cities in your question.