i have been in Chessington for about 6 years now & have only really got to know the area and met (apart from the neighbours)people since I had my son who is now 17 months. We lived here for 2 years before we even discovered the lovely Churchfields were only a 5 min walk from our house!!!
Ive not really heard of any bad nurserys or schools in chessington,
Castle hill has just moved to one site as a single Primary rather than infant & junior schools so needs a bit of time to get re-established and it has a fairly new head.
There is also another Primary school behind the Community college, I dont know what it called but I have seen parents dropping off & picking up their little ones there.
There is a childrens centre at Castle Hill school (Buckland Rd) which has different play groups and activities for families and under 5's and the King's Centre has a fantastic parent & toddler group "Rainbow tots" for under 5's for you to meet other mums in the area. (different to the Playmates Nursery)
The king centre is also a great place to go for bit of lunch or coffee although for most Chessington/Hook residents it is a bit out of the way. Its actually an evangelical church but dont let that put you off.
good luck with your settling in