You arrive in the afternoon and board the next day? Does the ship overnight in Shanghai or is your only time that one afternoon and the next day until sailaway?
I would get a driver and guide for a full day tour and transfer to the ship as a minimum. To be in Shanghai and not see the city would be a shame.
Must sees are Yu Yuan Garden, the Shanghai Museum, and the observation deck above your hotel. I would also try to see the Chinese Acrobat show the evening you are in town. You need to check out the Bund. Shopping is fantastic! Don't forget that you can legally bring in one illegal knockoff into the US. Watches, handbags, and pearls are short. The first two are knockoffs and the third are real. My wife bought Pearls for all of our female relatives last year at an average cost of arond $12 per strand.
Hopefully, Mike will stop in with more suggestions.