You could always try the old standby places like Shanghai Gongqing Forest Park and Acquaria 21 (underground aquarium), Jin Jiang Amusement Park, or a water park like Tropical Storm in the summertime. For cultural and educational outings I like the Shanghai Museum, Museum of Contemporary Art (MoCA), Shanghai Natural History Museum, and Shanghai Science and Technology Museum. The Railway and Natural Wild Insect Kingdom Museums are smaller but fun too. For younger kids (around 3-9 years), Eday Town educational centre is great for learning and having fun.

I live close to Century Park and I love to bring my child there every day for a walk....There are lots of green spaces, and some old fashioned roller-coaster. You can rent a bike or a boat.

Otherwise, the Science & Technology museum is great too. Mine is only 19 months old and I bring there to the Design section where he can play and touch things.

If you need other advices, let me know...