We are a british PR family and have been here for 4 years, and have a three year old son. As well as organised school activities you can.
1.Ride bikes along the East coast on proper bike tracks by the sea.
2.Ride on tracks around the nature reserves.
3.Go to Centre Stage on River Valley Road which has drama and music classes for 3years and over. It is exellent and run by Expats.
4.Use the British Club (Join)get a short trial membership and use kids facilities and classes.
5.Go to Downtown East and use the massive indoor Gym for small change.
6.Go to
www.sistic.com.sg regulary and buy tickets to all the kids shows, Hi5,Kids Central,Cartoon network etc.
7.Go to the Singapore Tourist info on Orchard Road and pick up loads of flyers for kids activities.
8.United Square on the corner of Thompson and Newton Road is a specialist kids shopping centre with Kinda Golf,Music classes ie piano,violin,drums,etc.plus fencing for tots ! far to much info. good luck.