It is possible to take a day trip to Suzhou or Hangzhou from Shanghai.
I went to Suzhou by train and took a sightseeing bus from the train station there.
As for Hangzhou a bus picked us up at the hotel at 7 in the morning and came back at 11 in the evening, that was quite hectic.
This was back in 2010 so things have probably changed, now there is a high speed train to Hangzhou I think.