Double decker buses are always a fun way to see the city. The Shanghai government has it's own bus running for only $3.5 a day. Make sure you use the one marked "CityBusTour" (instead of the competition that takes $35 for the same thing).
The "Les Passages" are filled with small quaint shops. A perfect place for a nice afternoon stroll on a rainy day.
The Wailing Wall is one of the most sacred places to Jews. Archaeologist have dug out the old remains of the wall so you can walk the caves below the wall to witness history with your own eyes.