Is a Transit visa require to transfer from Pudong (PVG) airport to Hongqiao (SHA) Airport?

We are travelling from India to taiwan and have a 21 hours stopover at shanghai. Our flight from India, however, arrives at the pudong airport while our flight to taiwan leaves from Hongqiao. Would we require a transit visa or any other type to transfer from these airports? I would also like to know what the costs for the same would be, if any. Would it be possible for us to travel around shanghai for a few hours during this period and what would be the requirements for the same?