Boat ride along the Bund.

The somewhat tacky history of Shanghai museum in the basement of the ??? tower on the Pudong side, almost next to the aquarium.

Go to some of the history of the communist party sites, such as former homes of some of the famous politicians. There's a nice museum in the Xiandu (spelling?) area, almost over the tea shop.

Explore the remains of the Shanghai Expo site.

Visit Chinese university campuses such as Fudan. The buildings look very different from a USA college campus.

Depending on interests, the antique stores (old game sets) along philosophers' walk and some of the poster stores in the French Connection or the art museum near people's square and the small contemporary art museum hidden at the back of the garden (behind the lilly pond) next door, perhaps combined with the (modern) architecture of the theater/opera house and some of the nearby hotels such as LRM. [LRM has an amazing koi tank near the entrance to the Chinese restaurant on about the fourth floor. There once was a similar fish tank in the old department store across the street, but it's gone now. Walk toward the water from LRM and check out all of the street performances. Along the Bund, look for kites and groups doing dance exercises in unison.] Maybe include a brief visit to the Shanghai museum, but IMO that would be a tougher sell for a kid.

Take a ride on the Maglev if it wasn't used to/from the airport. Maybe check out the newest subway line too, or try to see the high speed trains, but I'm not sure you can get close without buying tickets.

There are some museums out of the way on the Pudong side, IIRC including a science museum.