I would like to seek your advice. I have 2 days in early Nov to spare in Shanghai. What would be the must see places

I think the Bund, the Nanjing Road, Yuyuan Garden, SH Museum, Oriental Pearl TV Tower, World Financial Center and the Jade Buddha Temple are worth seeing.
If you are interested in water towns, it is suggested to go to the Zhujiajiao Water Town and spend about one day there.

Thanks. Another concern. How can I go from ZJJ or Shanghai city to Putong International Airport by public transport?

From ZJJ, you need to take the Huzhu Line to go back to the People's Square in the city downtown area. Upon reaching the People's Square, you can use the local subway lne 2 to go back to the airport directly.
From SH city, you can use subway line 2 or the airport shuttle bus to reach the airport. Shuttle bus line 1 can be taken at Jing'an Temple area and the line 5 can be taken near the local railway station.