Help to make sure we don't miss anything or waste time

I am meeting up with a friend on the way home and have 6 days in Shanghai at the end of this month. I would like to expolre as much as possible without doing arranged tours the whole time. Do you have a suggestions. I would like to find a foodie type day with local cooking school or similar. Have fabrice markets and silk factory etc covered in a one day tour.
Very interested in old parts of the city as well as the new. Previous have only spent two days in the city. any suggestions mosty welcome. many thanks