Some more random ideas:

Old China hand reading room on Shaoxing Road.. beautiful books on art and architecture you can look at over a pot of tea.. the street is a small street in the French concession..

Two free museums
ShanghaI Municipal Archives on the Bund ..history of Shanghai developing into a city..there has never been anyone there when we've been there
Postal Museum ..interesting building the former post office, stamps, mailboxes, communication methods and how they changed I know it might sound boring, but the exhibits and the English translations are really interestung

Ride on the river..do it at dusk to see the buildings in daytime and as the light show starts at night

You will have a great time