It is basically impossible to buy a house in Shanghai with two million. Even outside the most remote outer ring, you can only buy a small apartment of about 60 square meters. Of course, if it is used as a down payment, that is enough.

Whether you want to stay in Shanghai or go to another place depends on other circumstances and a detailed analysis. The key is to see where is more suitable for your life and work. Buying a house or not buying a house is the next best thing.