This has been in the draft for ever so just posting now. It might be useful for people living in Basavangudi or Banashankari stage I. I have tagged the location of the park you can check out the directions. It is a nice huge park with a few things for the amusement of kids.
There is a train too but while I was in Blr. it was still not operating.
There a face that gurgles out water
There are lots of jungle gyms and statues of Dinosaurs and plants shaped as animals.
Since the terrain is uneven walking around is as enjoyable as a trek. Some pics here that might interest your kid.