Any recommendations for child-friendly activities to do or places to go in Singapore over weekend, other than going to shopping malls?

For us, we like to bring kids to public swimming pool weekly. There are a lot of free water play areas in Singapore e.g. Science Centre, Botanic Garden, Garden By the Bay. In addition, you can bring kids to zoo, river safari, bird park. You can sign up membership to visit these places frequently. If you have running out of ideas, you can purchase Kevin Ang's book: Got Kids Go Where from Mothercare.