Still exploring this city but here's what I've done so far. To get around, set up Didi on your phone (Uber/Lyft don't work) or get yourself a Shanghai Metro card from a service desk.
Samir L: Take the Maglev for 40 RMB to/from the airport with your Shanghai Metro card. Runs at 300 km/h most hours, except 430 km/h from 9-10:45 and 3-3:45 each day.
Samir L: Beautiful traditional Chinese gardens - you can wander here for hours. Surrounding the gardens is a bustling shopping district with lots of street food options and cafes.
Samir L: Gallery after gallery -- you'll find a lot of styles repeated from place to place, so come with some patience and you might walk out with an affordable and stylish art piece to your liking.