Get breakfast at the Nan Xiang Soup Dumpling place here and visit Yu Garden to see the classic "jiang nan" garden architecture
Tian Zi Fang is a more authentic representation of the traditional residential stone houses in Shanghai. I like the galleries, boutiques and desserts here.
This is a great restaurant in SML right outside of Tian Zi Fang. There is usually a long wait but worth it.
West Nanjing Road is the top shopping area in Shanghai. The luxury at Plaza 66 is definitely world class. Also, find Yang's Fried Dumplings on the way - it is the best. Period.
Check out the Art Museum while you walk along the West Nanjing Road. Very different collections from the western galleries.
Keep walking east on Nanjing Road will bring you to the center of Shanghai. Very touristy spot but a lot to see.
Definitely go to the bund when it's dark and see one of the most amazing skylines and lightings in the world!
Good luck getting in!