I don't know about Shanghai, but when my boys turned 3 I held their party on a university campus.  There was lots of green space for them and their friends to run around and have fun.  We didn't get any hassles from the students or security, so a good time was had by all.

Of course, we just had a small group of around 12 people total and nothing crazy like bouncy castles or stuff like that.

I am not sure if they do parties at Mcdonalds I know they do in the U.K lots of kids have them there

Indoor playgrounds, almost every shopping mall has one nowadays. Afterwards you go to the KFC or McDonalds. Plenty of things you can do and depends on your budget too.

There is a indoor place called "Lollipop" at Lianyang Plaza in Pudong, where you can organize a party for children.
The place itself is a kind of indoor playground with many games for children to play, jump, shoot, slide, etc.

Best bets- MacDonalds and KFC

Is there a Chucky Chinese Cheese?

For a three year old have a house party. Hire a clown and bring over some friends. Bring lots of gifts fill the house with balloons and decorations. Get a cake and some icecream!