It's not my first post, but the Singapore Science Centre was my first stop after leaving the airport. It's located on the other side of town from the airport, but I got there pretty easy with only a couple train changes.
Opening hours are 10:00-18:00 daily, though they generally close one day a month. Check the website for the schedule. Also at the Science Centre is something called KidsSTOP (a children's science-focused play center), an Omni-Theatre IMAX), and Snow City (an indoor snow play center), so it's possible to stretch this place out into a full day with little ones.
Standard admission to the Science Centre is $12.00, $15 with the Human Body Experience. Prices for the other places vary.
Note that the Science Centre will be moving into a new building around 2020, not too far away.